Journées ANR HEAD

Liste des Contributions

2. Large-time stability of partially dissipative hyperbolic systems

Timothée Crin-Barat

13/04/2026 16:00

In this talk, we consider hyperbolic systems with dissipative effects arising from viscosity or friction. We start by reviewing recent results on the stability of perturbations around constant equilibria. Then, we discuss how the stability analysis changes when passing from constant states to space-periodic traveling waves. In this setting, we introduce a space-averaged Shizuta–Kawashima-type...

3. A hyperbolic dispersive model for coastal waves

Maria Kazakova (LAMA, USMB)

13/04/2026 17:00

A shallow water model for the propagation and breaking of surface waves is proposed, under the form of a hyperbolic system of conservation laws, with dispersive effects introduced through a relaxation term and with a localized dissipative term. The latter is activated in regions where a breaking criterion is met. The objective is to get a simple mathematical and numerical structure while...

4. Mini-course 1: on discrete integration by parts methods

Jean-François Coulombel (Institut de Mathématiques de Toulouse)

14/04/2026 09:00

The course will review several aspects of discrete integration by parts methods. The ultimate goal is to construct finite difference approximations of the first order derivative that satisfy a similar integration by parts formula as in the continuous setting on a half-line. Basic questions (and partial answers) include existence, uniqueness and non-existence results. We shall connect the...

5. Mini-course 1: on discrete integration by parts methods

Jean-François Coulombel (Institut de Mathématiques de Toulouse)

14/04/2026 10:45

The course will review several aspects of discrete integration by parts methods. The ultimate goal is to construct finite difference approximations of the first order derivative that satisfy a similar integration by parts formula as in the continuous setting on a half-line. Basic questions (and partial answers) include existence, uniqueness and non-existence results. We shall connect the...

6. Asymptotic-preserving schemes

Marie-helene Vignal (Institut de Mathématiques de Toulouse, Université Toulouse 3 - Paul Sabatier)

14/04/2026 14:00

In this presentation, I will begin by explaining the objectives and underlying principles of asymptotic-preserving schemes. I will then focus on two specific cases: schemes that preserve the low Mach number limit for the Euler equations, and schemes that preserve the quasi-neutral limit for the Vlasov–Poisson equations. I will discuss the main challenges in simulating these problems...

7. Are $L^\infty$ solutions to hyperbolic systems of conservation laws unique?

Sam Krupa (Ecole Normale Supérieure)

14/04/2026 15:00

For hyperbolic systems of conservation laws in 1-D, fundamental questions about uniqueness and blow up of weak solutions still remain even for the apparently “simple” systems of two conserved quantities such as isentropic Euler and the p-system. Similarly, in the multi-dimensional case, a longstanding open question has been the uniqueness of weak solutions with initial data corresponding to...

8. Dispersionless limit in the Euler-Korteweg system

Corentin Audiard (Sorbonne Universite)

14/04/2026 16:30

The Euler-Korteweg equations are a modification of the Euler equations which include in the momentum equation a term modelling capillary forces. Mathematically, this supplementary term is of dispersive nature, and after a reformulation the system looks like a degenerate Schrödinger equation. We consider here the behaviour of smooth solutions when the capillary coefficient is very small. When...

9. Mini-course 2: orbital stability of periodic waves in Hamiltonian systems under localized perturbations

Björn de Rijk (Karlsruher Institut für Technologie)

15/04/2026 09:00

In Hamiltonian systems, periodic waves often correspond to coherent structures: recurrent, robust patterns that persist over time. Notable examples include water waves, periodic sequences of light pulses in nonlinear optical fibers, and soliton trains in Bose-Einstein condensates. To date, nonlinear stability results for periodic standing or traveling waves in Hamiltonian systems have...

10. Mini-course 2: orbital stability of periodic waves in Hamiltonian systems under localized perturbations

Björn de Rijk (Karlsruher Institut für Technologie)

15/04/2026 10:45

In Hamiltonian systems, periodic waves often correspond to coherent structures: recurrent, robust patterns that persist over time. Notable examples include water waves, periodic sequences of light pulses in nonlinear optical fibers, and soliton trains in Bose-Einstein condensates. To date, nonlinear stability results for periodic standing or traveling waves in Hamiltonian systems have...

11. Simple non-linear behaviors in models of climate phenomena

Gilles Bellon (Centre National de Recherches Météorologiques)

15/04/2026 14:00

Although the climate system is inherently chaotic, many idealized models employed in climate science display behaviors characteristic of low-dimensional nonlinear dynamical systems. Even models incorporating more comprehensive and detailed physical processes may reproduce similar behaviors in idealized configurations. Such models provide valuable conceptual frameworks for understanding modes...

12. Global well-posedness and asymptotic behavior of an inviscid non-equilibrium radiation hydrodynamics system

José Manuel Valdovinos (Institut de Mathématiques de Toulouse)

15/04/2026 15:00

We consider the one-dimensional diffusion approximation, non-equilibrium model of radiation hydrodynamics derived by Buet and Després (J. Quant. Spectrosc. Radiat. Transf. 85 (2004), no. 3-4, 385–418). This system describes a non-relativistic inviscid fluid subject to a radiative field under the non-equilibrium hypothesis, that is, when the temperature of the fluid is different from the...

13. Variations on the Gatenby-Gawlinski model for acid-mediated tumour growth

Corrado Mascia (Sapienza Università di Roma)

15/04/2026 16:30

For evident reasons, Cancer Biology is one of the most challenging topics of current medical research and understanding the mechanism behind its uncontrolled growth is a crucial issue. Among other explanations of the process, the Warburg effect posits that a pivotal role is played by the so-called aerobic glycolysis, i.e. the fact that, even in presence of oxygen, lactic acid fermentation can...

14. Mini-course 3: symmetrizers

Antoine Benoit (ULCO)

16/04/2026 09:00

The aim of this lecture is to present new results concerning the well-posedness of hyperbolic systems defined in a domain with a corner. In the canonical half-space geometry, Kreiss’s theory [1970] characterizes well-posed problems in terms of an algebraic condition, the so-called uniform Kreiss–Lopatinskii condition. The main contribution of Kreiss’s work is the construction of a so-called...

15. Mini-course 3: symmetrizers

Antoine Benoit (ULCO)

16/04/2026 10:45

The aim of this lecture is to present new results concerning the well-posedness of hyperbolic systems defined in a domain with a corner. In the canonical half-space geometry, Kreiss’s theory [1970] characterizes well-posed problems in terms of an algebraic condition, the so-called uniform Kreiss–Lopatinskii condition. The main contribution of Kreiss’s work is the construction of a so-called...

16. Discrete hypocoercivity for a nonlinear kinetic reaction model

Marianne Bessemoulin-Chatard (Laboratoire de Mathématiques Jean Leray)

16/04/2026 14:00

In this talk, I will present a finite volume discretization of a 1D nonlinear kinetic reaction model, which describes a two-species recombination-generation process. More specifically, we establish the long-time convergence of the approximate solutions to equilibrium, at an exponential rate. To do this, we adapt the proof proposed in [Favre, Pirner, Schmeiser, ARMA 2023], based on an...

17. Emergence of peaked singularities in the Euler-Poisson system

Junsik Bae (Kyungpook National University)

16/04/2026 15:00

We consider the one-dimensional Euler-Poisson system equipped with the Boltzmann relation. We provide the exact asymptotic behavior of the peaked solitary wave solutions near the peak. This enables us to study the cold ion limit of the peaked solitary waves with the sharp range of Holder exponents. Furthermore, we provide numerical evidence for $C^1$ blow-up solutions to the pressureless...

18. Hyperbolic regularization effects for degenerate elliptic equations

Xavier Lamy (Institut de Mathématiques de Toulouse)

16/04/2026 16:30

Among weak solutions of Burgers' equation, a single strictly convex entropy is sufficient to characterize the sign of all entropy productions. In particular, if that entropy production vanishes, then the solution must be continuous. It turns out that this fact can be interpreted as a regularity result for a degenerate elliptic equation in the plane, and generalized to prove partial regularity...

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