A Picard-Maclaurin theorem for initial value PDEs.
Almost global existence of small solutions to quadratic nonlinear Schördinger equations in three space dimensions.
An abstract non-linear Cauchy-Kowalewski theorem and its proof by a contraction-mapping principle
An Age and Spatially Structured Population Model for Proteus Mirabilis Swarm-Colony Development
Proteus mirabilis are bacteria that make strikingly regular spatial-temporal patterns on agar surfaces. In this paper we investigate a mathematical model that has been shown to display these structures when solved numerically. The model consists of an ordinary differential equation coupled with a partial differential equation involving a first-order hyperbolic aging term together with nonlinear degenerate diffusion. The system is shown to admit global weak solutions.
Asymptotic behavior for a quadratic nonlinear Schrödinger equation.
Asymptotic behaviour in time of solutions to some equations generalizing the Korteweg-de Vries-Burgers equation
Asymptotic profile of solutions for the critical Sobolev type equation on a half-line.
Asymptotics for , II. Scattering theory
Asymptotics for I. Global existence and decay
Attractivity of nonlinear impulsive delay differential equations.
Conservation laws for equations related to soil water equations.
Construction de solutions ramifiées autour de deux hypersurfaces caractéristiques simples pour des opérateurs quasi-linéaires
Continuous selections of solution sets to second order evolution equations.
Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics
We prove the convergence at a large scale of a non-local first order equation to an anisotropic mean curvature motion. The equation is an eikonal-type equation with a velocity depending in a non-local way on the solution itself, which arises in the theory of dislocation dynamics. We show that if an anisotropic mean curvature motion is approximated by equations of this type then it is always of variational type, whereas the converse is true only in dimension two.
Counterexamples to Hölmgren's uniqueness for analytic non linear Cauchy problem.
Die Lösung der partiellen Differentialgleichung mit gewissen Nebenbedingungen
Existence and limiting behaviour for damped nonlinear evolution equations with nonlocal terms
Existence and Uniqueness of Solutions for the Generalized Korteweg de Vries Equations.
Existence theorems for a partial differential equation of the fourth order
Finite difference approximations for nonlinear first order partial differential equations.