An ill posed Cauchy problem for a hyperbolic system in two space dimensions
An L¹-stability and uniqueness result for balance laws with multifunctions: a model from the theory of granular media
We study the uniqueness and L¹-stability of the Cauchy problem for a 2 × 2 system coming from the theory of granular media [9,10]. We work in a class of weak entropy solutions. The appearance of a multifunction in a source term, given by the Coulomb-Mohr friction law, requires a modification of definition of the weak entropy solution [5,6].
Analysis of Synchronization in a Neural Population by a Population Density Approach
In this paper we deal with a model describing the evolution in time of the density of a neural population in a state space, where the state is given by Izhikevich’s two - dimensional single neuron model. The main goal is to mathematically describe the occurrence of a significant phenomenon observed in neurons populations, the synchronization. To this end, we are making the transition to phase density population, and use Malkin theorem to calculate...
Analysis tools for finite volume schemes
Apparition éventuelle de singularités dans des problèmes d'évolution non linéaires
Arbitrary Lagrangian Eulerian method for compressible plasma simulations
Asymptotic behavior for the centered-rarefaction appearance problem.
Asymptotic behavior of solutions of a system of viscous conservation laws.
Asymptotic behaviour of solutions to nonlinear parabolic equations with variable viscosity and geometric terms.
Asymptotic time-behavior for weighted scalar conservation laws
Asymptotics for conservation laws involving Lévy diffusion generators
Let -ℒ be the generator of a Lévy semigroup on L¹(ℝⁿ) and f: ℝ → ℝⁿ be a nonlinearity. We study the large time asymptotic behavior of solutions of the nonlocal and nonlinear equations uₜ + ℒu + ∇·f(u) = 0, analyzing their -decay and two terms of their asymptotics. These equations appear as models of physical phenomena that involve anomalous diffusions such as Lévy flights.