The thematic session, "Partial Differential Equations - Methods, Computing and Applications", organized by Eduardo Abreu (UNICAMP, Brazil), Patricia Saavedra Barrera (Universidad Autónoma Metropolitana, Mexico) has been accepted for the First Joint Meeting Brazil-Mexico in Mathematics 2025.

SITE: https://sbm.org.br/jointmeeting-mexico/.

DATE:  September 8th to 12th 2025

WHERE:  Fortaleza, CE, Brazil

The Brazilian Mathematical Society (SBM) and the Brazilian Society for Computational and Applied Mathematics (SBMAC) are honored to invite the mathematical community to take part in the first Brazil-Mexico Joint Mathematical Meeting, which will be held in Fortaleza, Brazil, from September 8 to 12, 2025. This event is a partnership with the Mexican Mathematical Society (SMM) https://sbm.org.br/jointmeeting-mexico/welcome/

International Congress of Mathematicians (ICM) 2026 , Philadelphia, USA, 23th to 30th July 2026

https://www.mathunion.org/icm/icm-2026

ICM 2026 will be hosted at the Pennsylvania Convention Center in Philadelphia over 23–30 July 2026.

The 20th IMU General Assembly will convene at the Marriott Marquis Times Square over 20–21 July 2026.

International Mathematical Union (IMU) Home ==> https://www.mathunion.org/

Mathematical Congress of the Americas 2025: July 21, 2025 – July 25, 2025

The goal of the Mathematical Congress of the Americas (MCA) is to internationally highlight the excellence of mathematical achievements in the Americas and foster collaborations among researchers, students, institutions and mathematical societies in the Americas.

LINK: https://www.mca2025.org/event/9e9666dd-2643-423b-b343-91f10f36e686/summary

Special Sessions: https://www.mca2025.org/event/9e9666dd-2643-423b-b343-91f10f36e686/websitePage:f3552742-6e9a-44e3-a319-6b6056ba9900

In the Mathematical Congress of the Americas (MCA), take a look at

Session 38: Conservation Laws: Mathematical and Numerical Analysis with Applications

Organizers:

Eduardo Abreu (Universidade Estadual de Campinas, Brazil, contact organizer)
Fabio Ancona (University of Padua, Italy)
Maria Teresa Chiri (Queen’s University, Canada)
Xiaoqian Gong (Amherst College, USA)
Michael Herty (RWTH Aachen University, Germany)

Brief Summary: Hyperbolic conservation laws have been subject to extensive analytical and numerical studies over the last decades. It is widely known that their solutions can exhibit very complex behavior including the simultaneous presence of smooth waves, wave breaking, and shock waves. These equations describe the conservation of some basic physical quantities of a system, and they arise in all branches of science and engineering: from fluid dynamics to vehicular traffic modeling. The scope of this Special Session is to bring together researchers with interests in the theoretical, applied, and computational aspects of hyperbolic partial differential equations with real-life applications and discuss the state of the art of the field.

In the perspective of accomplishing the goals of the 2025 Mathematical Congress of the Americas (MCA2025), the invited speakers are of different ages, nationalities, and different scientific career stages and they are selected among the leaders in the field. This aspect makes the Special Session suitable for training young researchers and fostering interactions between several mathematical communities across the Americas (South, Central and North).

 The following work have been accepted for publication on "CALCOLO" (https://link.springer.com/article/10.1007/s10092-024-00624-x):

A numerical scheme for doubly nonlocal conservation laws

E. Abreu, J. C. Valencia-Guevara, M. Huacasi-Machaca & J. Pérez.

Published: 22 November 2024; Volume 61, article number 72, (2024).

Keywords: Fractional conservation laws. Doubly nonlinear nonlocal flux. Riesz potential. Hilbert transform. Numerical algorithm for the Riesz fractional Laplacian. Nonlocal Lagrangian–Eulerian scheme. Nonlocal no-flow curves.

Mathematics Subject Classification: 47G40. 47B34. 65Y20. 35R11. 35B44.

Highlights:
In this work, we consider the nonlinear dynamics and computational aspects for nonnegative solutions of one-dimensional doubly nonlocal fractional conservation laws

∂tu + ∂x [uA^α−1(κ(x)Hu)] = 0 and ∂tu − ∂x [uA^α−1(κ(x)Hu)] = 0,

where A^α−1 denotes the fractional Riesz transform, H denotes the Hilbert transform, and κ(x) denotes the spatial variability of the permeability coefficient in a porous medium. We construct an unconventional Lagrangian–Eulerian scheme, based on the concept of no-flow curves, to handle the doubly nonlocal term, under a weak CFL stability condition, which avoids the computation of the derivative of the nonlocal flux function. Primarily, we develop a feasible computational method and derive error estimates of the approximations of the Riesz potential operator A^α−1. Secondly, we undertake a formal numerical-analytical study of initial value problems associated with such doubly nonlocal models to add insights into the role of nonlinearity and coefficient κ(x) in the composition between the Hilbert transform and the fractional Riesz potential. Numerical experiments are presented to show the performance of the approach.

 

25 anos do Bacharelado em Matemática Computacional da UFMG

Semana da MatComp: 18, 19 e 21 de novembro de 2024

Dia Comemorativo: 22 de novembro de 2024

HOMEPAGE:  https://www.matcomp25anos.dcc.ufmg.br/

Palestra Convidada: "Eduardo Abreu: Análise numérica para modelos diferenciais: sinergia natural entre contínuo e discreto na matemática e aplicações"

LINK:  https://www.matcomp25anos.dcc.ufmg.br/#palestras

The following work have been accepted for publication on "Numerical Methods for Partial Differential Equations" and it will available online soon (MNPDE, https://onlinelibrary.wiley.com/journal/10982426):

An enhanced Lagrangian-Eulerian method for a class of balance Laws: numerical analysis via a weak asymptotic method with applications

Eduardo Abreu, Eduardo Pandini and Wanderson José Lambert.

Highlights:
In this work, we designed and implemented an enhanced Lagrangian-Eulerian numerical method for solving a wide range of nonlinear balance laws, including systems of hyperbolic equations with source terms. We developed both fully discrete and semi-discrete formulations, and extended the concept of No-Flow curves to this general class of nonlinear balance laws. We conducted a numerical convergence study using weak asymptotic analysis, which involved investigating the existence, uniqueness, and regularity of entropy-weak solutions computed with our scheme. The proposed method is Riemann-solver-free. To evaluate the shock capturing capabilities of the enhanced Lagrangian-Eulerian  numerical scheme, we carried out numerical experiments that demonstrate its ability to accurately resolve the key features of balance law models and hyperbolic problems. A representative set of numerical examples is provided to illustrate the accuracy and robustness of the proposed method.

ISAAC-ICMAM Conference of Analysis in Developing Countries 2024.

https://www.matua.edu.co/isaac-icmam-conference-of-analysis-in-developing-countries-2024/

The ISAAC-ICMAM (Virtual) Conference of Analysis in Developing Countries represents a significant collaboration between ISAAC and ICMAM Latin America. This jointly organized conference aims to share mathematical research in Latin America and the Caribbean, enhance its visibility, and foster collaboration among mathematicians from the region and worldwide.

During the conference, the following speak will be presented by Eduardo Abreu (Universidade Estadual de Campinas, UNICAMP, Brazil):

Title: A forward-tracking Lagrangian-Eulerian method for multidimensional systems of conservation laws

Abstract: We will discuss a forward Lagrangian-Eulerian approach to undertake a numerical-analytical study of inherent properties of multidimensional nonlinear hyperbolic conservation laws [(2024)  https://doi.org/10.1016/j.cam.2023.115465]. It is widely known that their solutions can exhibit very complex behavior including the simultaneous presence of smooth waves, wave breaking, and shock waves. The novel forward tracking Lagragian-Eulerian formulation is based on the improved concept of no-flow curves. In the context of multidimensional hyperbolic systems of conservation laws, the resulting Lagrangian-Eulerian method satisfies a weak positivity principle in view of results of P. Lax and X.-D. Liu [Computational Fluid Dynamics Journal, 5(2) (1996) 133-156 and [Journal of Computational Physics, 187 (2003) 428-440]. We also found in [(2023) https://doi.org/10.1007/s10884-023-10283-1] a connection between the notion of no-flow curves, viewed as a vector field with locally bounded variation, and the results of A. Bressan in the context of existence and continuous dependence for discontinuous O.D.E.’s [Proc. Amer. Math. Soc. 104 (1988), 772-778]. We have tested the approach for well-known non-trivial muitlt-D systems and complex problems in fluid dynamics [(2023) https://doi.org/10.1016/j.amc.2022.127776,  (2023) https://link.springer.com/article/10.1007/s10915-021-01712-8 , (2021) https://doi.org/10.1007/s10915-020-01392-w]: 4 by 4 compressible Euler equations (Double Mach Reflection problem and Mach 3 wind tunnel flow, the 3 by 3 shallow-water system with and without bottom topography, and the 8 by 8 Orszag-Tang vortex system in magnetohydrodynamics and a nonclassical 2 by 2 three-phase flow system of non strictly hyperbolic conservation laws with a resonance/umbilic point.

ISAAC-ICMAM Conference of Analysis in Developing Countries 2024:

  

Matemáticas & Memoria: Un seminario de Análisis y Ecuaciones diferenciales para Latinoamérica.

Matemáticas y Memoria: Un seminario de Análisis y Ecuaciones diferenciales para Latinoamérica. – MATUA

El seminario «Matemáticas y memoria: un seminario de Análisis y Ecuaciones diferenciales para Latinoamérica» tiene como objetivo principal promover el intercambio de conocimientos y experiencias en el campo del análisis y las ecuaciones diferenciales, destacando la importancia de la memoria histórica en el desarrollo matemático de Latinoamérica. A través de la participación de invitados nacionales e internacionales, la visibilización de jóvenes talentos matemáticos y la invitación a reconocidos investigadores establecidos, se busca fomentar el diálogo académico y fortalecer la comunidad matemática regional.

Presentacíon de octubre: No-Flow Lagrangian-Eulerian Curves for Hyperbolic Conservation Laws. Eduardo Abreu (Universidade Estadual de Campinas, Brasil). LINK:  https://youtu.be/HQMibFXNnUg

Se puede acceder a las demás presentaciones en Matemáticas y Memoria: Un seminario de Análisis y Ecuaciones diferenciales para Latinoamérica. – MATUA.

Matemáticas y memoria: un seminario de Análisis y Ecuaciones diferenciales para Latinoamérica:

The following work have been accepted for publication on "Journal of Computational and Applied Mathematics" https://doi.org/10.1016/j.cam.2024.116325:

Semi-discrete Lagrangian-Eulerian approach based on the weak asymptotic method for nonlocal conservation laws in several dimensions

Eduardo Abreu, Richard A. De la Cruz Guerrero, Juan Carlos Juajibioy Otero and Wanderson José Lambert.

Highlights:
In this work, we have expanded upon the (local) semi-discrete Lagrangian-Eulerian method initially introduced in [E. Abreu, J. Francois, W. Lambert and J. Perez (2022), https://doi.org/10.1016/j.cam.2021.114011] to approximate a specific class of multi-dimensional scalar conservation laws with nonlocal flux. For completeness, we analyze the convergence of this method using the weak asymptotic approach introduced in [Eduardo Abreu, Mathilde Colombeau and Evgeny Yu Panov (2016), https://doi.org/10.1016/j.jmaa.2016.06.047], with significant results extended to the multidimensional nonlocal case. While there are indeed other important techniques available that can be utilized to prove the convergence of the numerical scheme, the choice of this particular technique (weak asymptotic analysis) is quite natural. This is primarily due to its suitability for dealing with the Lagrangian-Eulerian schemes proposed in this paper. Essentially, the weak asymptotic method generates a family of approximate solutions satisfying the following properties: 1) The family of approximate functions is uniformly bounded in the space L1(Rd) ∩ L∞(Rd) and 2) The family is dominated by a suitable temporal and spatial modulus of continuity. These properties allow us to employ the L1-compactness argument to extract a convergent subsequence. We demonstrate that the limit function is a weak entropy solution. Finally, we present a section of numerical examples in 1D and also in 2D for two-dimensional nonlocal Burgers equations to illustrate our results.

 

Mathematical Congress of the Americas 2025: July 21, 2025 – July 25, 2025

The goal of the Mathematical Congress of the Americas (MCA) is to internationally highlight the excellence of mathematical achievements in the Americas and foster collaborations among researchers, students, institutions and mathematical societies in the Americas.

LINK: https://www.mca2025.org/event/9e9666dd-2643-423b-b343-91f10f36e686/summary

Special Sessions: https://www.mca2025.org/event/9e9666dd-2643-423b-b343-91f10f36e686/websitePage:f3552742-6e9a-44e3-a319-6b6056ba9900

In the Mathematical Congress of the Americas (MCA), take a look at

Session 38: Conservation Laws: Mathematical and Numerical Analysis with Applications

Organizers:

Eduardo Abreu (Universidade Estadual de Campinas, Brazil, contact organizer)
Fabio Ancona (University of Padua, Italy)
Maria Teresa Chiri (Queen’s University, Canada)
Xiaoqian Gong (Amherst College, USA)
Michael Herty (RWTH Aachen University, Germany)

Brief Summary: Hyperbolic conservation laws have been subject to extensive analytical and numerical studies over the last decades. It is widely known that their solutions can exhibit very complex behavior including the simultaneous presence of smooth waves, wave breaking, and shock waves. These equations describe the conservation of some basic physical quantities of a system, and they arise in all branches of science and engineering: from fluid dynamics to vehicular traffic modeling. The scope of this Special Session is to bring together researchers with interests in the theoretical, applied, and computational aspects of hyperbolic partial differential equations with real-life applications and discuss the state of the art of the field.

In the perspective of accomplishing the goals of the 2025 Mathematical Congress of the Americas (MCA2025), the invited speakers are of different ages, nationalities, and different scientific career stages and they are selected among the leaders in the field. This aspect makes the Special Session suitable for training young researchers and fostering interactions between several mathematical communities across the Americas (South, Central and North).

The following work have been accepted for publication on "Computers and Mathematics with Applications" https://doi.org/10.1016/j.camwa.2024.04.015

Mathematical properties and numerical approximation of pseudo-parabolic systems

E. Abreu,  E. Cuesta, A. Duran and W. Lambert.

Highlights:
The paper is concerned with the mathematical theory and numerical approximation of systems of partial differential equations (pde) of hyperbolic, pseudo-parabolic type. Some mathematical properties of the initial-boundary-value problem (ibvp) with Dirichlet boundary conditions are first studied. They include the weak formulation, well-posedness and existence of traveling wave solutions connecting two states, when the equations are considered as a variant of a conservation law. Then, the numerical approximation consists of a spectral approximation in space based on Legendre polynomials along with a temporal discretization with strong stability preserving (SSP) property. The convergence of the semidiscrete approximation is proved under suitable regularity conditions on the data. The choice of the temporal discretization is justified in order to guarantee the stability of the full discretization when dealing with nonsmooth initial conditions. A computational study explores the performance of the fully discrete scheme with regular and nonregular data.

Keywords: Pseudo-parabolic equations, spectral methods, error estimates, strong stability preserving methods, non-regular data.

VII Congresso Latino-Americano e do Caribe de Matemática CLAM 2024

https://www.umalca.org/2023/08/clam-2024/

Session title: "Conservation laws: mathematical analysis and industrial-based models"
LINK: http://www.mat.ufpb.br/clam/index.php/atividades/sessoes-tematicas

Coordinators:
Aparecido Souza - UFPB - Brazil
Úrsula Iturrarán Viveros - UNAM - México
Pablo Castañeda - ITAM -  - México
Eduardo Abreu - IMECC-UNICAMP - Brazil

Aims and Scope: The objective of the thematic session entitled "Conservation laws: mathematical analysis and industrial-based models'', under the auspicious of the "VII Congreso Latinoamericano y del Caribe de Matemática'', is to bring together researchers from various fields with a central focus in mathematics with interests in the theoretical, applied, and computational aspects of hyperbolic partial differential equations and of related mathematical industrial-based models and some current trends. The research program focuses on an important synergy that engages several researchers and includes experts on modelling, analysis and computation to conservation laws. This aspect makes this field eminently suitable to train young researchers in and foster interactions between mathematical disciplines from an affirmative perspective to scientific development of countries in Latin American and Caribbean.

The following work have been accepted for publication on Communications in Nonlinear Science and Numerical Simulation (CNSNS; https://www.sciencedirect.com /journal/communications-in-nonlinear-science-and-numerical-simulation) and is now available online:

A relaxation approach to modeling properties of hyperbolic-parabolic type models

Eduardo Abreu, Wanderson Jose Lambert, Arthur Miranda do Espírito Santo and John Perez.

LINK: https://doi.org/10.1016/j.cnsns.2024.107967

Highlights:
• We propose a novel relaxation approach for modeling convection-diffusion problems via a hyperbolic system.
• The new system satisfies Liu’s sub-characteristic condition, ensuring solution stability.
• We apply the relaxation modeling to both classical and non-classical models.
• From numerical experiments, we verify the new system’s solutions converge to those of the original equations.

Keywords: Modeling using PDEs via Relaxation; Liu sub-characteristic condition; Convection-diffusion problems; Discontinuous flux function; Discontinuous coefficient in space; Numerical validation of models.

 

Workshop in complex fluids and solid mechanics II - June 13, 2024

https://w3.math.uminho.pt/~zecarlos/complex/#preprogram

Host institution: Department of Mathematics, School of Sciences, University of Minho

This is the second edition of the Workshop in Complex Fluids and Solid Mechanics, to be held at the Centre of Mathematics of the University of Minho in the 13th of June 2024.

Aims and Scope: Complex Fluids and Solid Mechanics are of great interest and relevance to scientific research, experimental technologies, and industrial applications.  The main goal of this workshop is to foster discussion and collaboration among mathematicians with diverse backgrounds and a common interest in solving problems related to materials exhibiting complex behavior and properties.

We are pleased to share news from the ECCOMAS Congress 2024 to be held in Lisbon, Portugal, on 3th – 7th of June, 2024 and in particular the following Mini-Symposia:

MS215 - Advances in Numerical Methods for Shallow Water Equations and its Applications

Keywords: shallow water equations, computational fluid dynamics, free surface models

Organized by:

E. Bachini (University of Padua, Italy) and

M. Fois (Politecnico di Milano, Italy).

LINK: https://eccomas2024.org/event/area/4f3a2d93-5968-11ee-a4f3-000c29ddfc0c

MS005 - Deep Learning Computing

Keywords: Computing, Deep Learning, Partial Differential Equations

Organized by:

M. Castro (University of Malaga, Spain),

D. Pardo (University of the Basque Country (UPV/EHU), Spain) and

F. Chinesta (ENSAM Institute of Technology, France)

LINK: https://eccomas2024.org/event/area/4e9414ab-5968-11ee-a4f3-000c29ddfc0c

III Workshop de Equações Dispersivas da UFMG, 19 e 20 de fevereiro de 2024.

https://www.sites.google.com/view/3wed

O evento acontecerá na sala 3060 do Instituto de Ciências Exatas (ICEx).

O estudo das equações dispersivas não-lineares tem sido muito ativo nos últimos tempos. Equações desse tipo modelam diversos fenômenos em ciência natural, dentre eles podemos destacar a teoria de ondas em fluidos, óptica não-linear, mecânica quântica.

Para mais detalhes sobre o III Workshop de Equações Dispersivas da UFMG 2024, ver o site oficial do evento:

SITE: https://www.sites.google.com/view/3wed

The following work have been accepted for publication on Journal of Hyperbolic Differential Equations (JHDE; https://www.worldscientific.com/doi/10.1142/S0219891624500012) and will available online soon:

Riemann problem solutions for a balance law under Dirac-Delta source with a discontinuous flux.

Eduardo Abreu, Vítor Matos, John Perez and Panters Rodriguez-Bermudez.

Keywords: Conservation laws; Discontinuous flux; δ-Dirac; Uniqueness of weak entropy solutions; Non viscous solutions; No-flow Lagrangian-Eulerian approach.

 

InterPore 2024 - SITE https://events.interpore.org/event/46/

16th annual meeting of International Society for Porous Media

Dates: Monday, May 13, 2024 - Thursday, May 16, 2024

Venue: Shangri-La Hotel Qingdao, Qingdao, China

The Focus Theme of InterPore2024 will be “porous media and biology.”

This includes occurrence and applications of biology in living organs, plants, and in medicine,

as well as in soil, oil and gas reservoirs. It will include theories and (bio)physics, experiments,

imaging, mathematics, and modelling.

The following work have been published an it is now available in the latest volume of Journal of Computational and Applied Mathematics: Volume 437, February 2024, 115465, ISSN 0377-0427.

A triangle-based positive semi-discrete Lagrangian–Eulerian scheme via the weak asymptotic method for scalar equations and systems of hyperbolic conservation laws

Eduardo Abreu, Jorge Agudelo, John Pérez.

LINK:  https://doi.org/10.1016/j.cam.2023.115465

Keywords: Hyperbolic conservation laws; Lagrangian–Eulerian method; Semi-discrete scheme on triangular grids; Weak asymptotic analysis; Kruzhkov entropy solution; Positivity principle

 

International Congress of Mathematicians (ICM) 2026 , Philadelphia, USA, 23th to 30th July 2026

https://www.mathunion.org/icm/icm-2026

ICM 2026 will be hosted at the Pennsylvania Convention Center in Philadelphia over 23–30 July 2026.

The 20th IMU General Assembly will convene at the Marriott Marquis Times Square over 20–21 July 2026.

International Mathematical Union (IMU) Home ==> https://www.mathunion.org/