Abstract Quasilinear Parabolic Equations.
Algorithmic construction of hyperfunction solutions to invariant differential equations on the space of real symmetric matrices.
Almost global existence of small solutions to quadratic nonlinear Schördinger equations in three space dimensions.
Almost-Everywhere Regularity Results for Solutions of Non Linear Elliptic Systems.
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.
An approach based on matrix polynomials for linear systems of partial differential equations
In this paper, an approach based on matrix polynomials is introduced for solving linear systems of partial differential equations. The main feature of the proposed method is the computation of the Smith canonical form of the assigned matrix polynomial to the linear system of PDEs, which leads to a reduced system. It will be shown that the reduced one is an independent system of PDEs having only one unknown in each equation. A comparison of the results for several test problems reveals that the method...
An efficient applications of He's variational iteration method based on a reliable modification of Adomian algorithm for nonlinear boundary value problems.
An eigenvalue problem for the complex Monge-Ampère operator in pseudoconvex domains
An existence result for nonlinear evolution equations of second order
In this paper we consider a second order differential equation involving the difference of two monotone operators. Using an auxiliary equation, a priori bounds and a compactness argument we show that the differential equation has a local solution. An example is also presented in detail.
An existence result for partially regular weak solutions of certain abstract evolution equations, with an application to magneto-hydrodynamics.
An existence theorem for the v. Kármán equations under the condition of free boundary
An inhomogeneous Dirichlet problem for a non-hypoelliptic linear partial differential operator.
An initial boundary value problem for Maxwell's equations in a parabolic limit case.
An iteration method for nonlinear second order evolution equations
An -analogue of the Vishik-Eskin theory.
Analyse mathématique de modèles variationells en simulation pétrolière. Le cas du modèle black-oil pseudo-compositionnel standard isoterme.
The aim of the paper is an analytical and numerical approach to the pseudo-compositional black-oil model for simulating a 3-D isothermal constrained polyphasic flow in porous media, taking into account realistic boundary conditions. The handling of the component conservation laws leads to a strongly coupled system including parabolic quasilinear degenerated equations and first-order hyperbolic inequalities: the introduction of unilateral problems arises from the nature of the thermodynamical equilibrium...
Analysis of a mathematical model related to Czochralski crystal growth.
Analytic approximation for homogeneous solutions of linear PDE's
Analyticity and smoothing effect for the Schrödinger equation