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.