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A nonlinear degenerate parabolic equation

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

A note on measure-valued solutions to the full Euler system

Applications of Mathematics

We construct two particular solutions of the full Euler system which emanate from the same initial data. Our aim is to show that the convex combination of these two solutions form a measure-valued solution which may not be approximated by a sequence of weak solutions. As a result, the weak* closure of the set of all weak solutions, considered as parametrized measures, is not equal to the space of all measure-valued solutions. This is in stark contrast with the incompressible Euler equations.

A note on the moving hyperplane method.

Electronic Journal of Differential Equations (EJDE) [electronic only]

A semilinear equation in ${L}^{1}\left({ℝ}^{N}\right)$

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Addition de variables et application à la régularité

Annales de l'institut Fourier

On montre dans cet article comment des théorèmes récents d’hypoellipticité ou de propagation des singularités peuvent être améliorés par une méthode d’addition de variables qui permet dans certains cas de “désingulariser” l’ensemble caractéristique.

An elementary proof for one-dimensionality of travelling waves in cylinders.

Journal of Inequalities and Applications [electronic only]

Behaviour of the support of the solution appearing in some nonlinear diffusion equation with absorption

Numerical experiments suggest interesting properties in the several fields of fluid dynamics, plasma physics and population dynamics. Among such properties, we may observe the interesting phenomena; that is, the repeated appearance and disappearance phenomena of the region penetrated by the fluid in the flow through a porous media with absorption. The model equation in two dimensional space is written in the form of the initial-boundary value problem for a nonlinear diffusion equation with the effect...

Bergman Spaces For The Solutions Of Linear Partial Differential Equations.

Revista colombiana de matematicas

Boundary regularity of solutions of the inhomogeneous Cauchy-Riemann equations

Séminaire Équations aux dérivées partielles (Polytechnique)

Catastrophes and partial differential equations

Annales de l'institut Fourier

This paper outlines the manner in which Thom’s theory of catastrophes fits into the Hamilton-Jacobi theory of partial differential equations. The representation of solutions of a first order partial differential equation as lagrangian manifolds allows one to study the local structure of their singularities. The structure of generic singularities is closely related to Thom’s concept of the elementary catastrophe associated to a singularity. Three concepts of the stability of a singularity are discussed....

Ciertas propiedades de las ecuaciones diferenciales complejas con coeficients polinomicos

Revista colombiana de matematicas

Diffraction by convex bodies

Séminaire Équations aux dérivées partielles (Polytechnique)

Doubling properties for second order parabolic equations.

Annals of Mathematics. Second Series

Geometrische Eigenschaften der Lösungen der Differentialgleichung (1-zz)2wzz - n(n + 1) w= 0.

Journal für die reine und angewandte Mathematik

Global Bifurcation of Waves.

Manuscripta mathematica

Introduction

Séminaire sur les équations non linéaires (Choodnovsky)

Large time behavior in a density-dependent population dynamics problem with age structure and child care

Banach Center Publications

Two asexual density-dependent population dynamics models with age-dependence and child care are presented. One of them includes the random diffusion while in the other the population is assumed to be non-dispersing. The population consists of the young (under maternal care), juvenile, and adult classes. Death moduli of the juvenile and adult classes in both models are decomposed into the sum of two terms. The first presents death rate by the natural causes while the other describes the environmental...

Local properties of stationary solutions of some nonlinear singular Schrödinger equations.

Revista Matemática Iberoamericana

We study the local behaviour of solutions of the following type of equation,-Δu - V(x)u + g(u) = 0 when V is singular at some points and g is a non-decreasing function. Emphasis is put on the case when V(x) = c|x|-2 and g has a power-like growth.

Mean value and Harnack inequalities for a certain class of degenerate parabolic equations.

Revista Matemática Iberoamericana

In this paper we study the behavior of degenerate parabolic equations of the formv(x) ut(x,t) = Σni,j=1  Dxi (aij(x,t) Dxi u(x,t)),where the coefficients are measurable functions.

Multi-bump solutions for nonlinear Schrödinger equations with electromagnetic fields

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we are concerned with the existence of multi-bump solutions for a nonlinear Schrödinger equations with electromagnetic fields. We prove under some suitable conditions that for any positive integer m, there exists ε(m) &gt; 0 such that, for 0 &lt; ε &lt; ε(m), the problem has an m-bump complex-valued solution. As a result, when ε → 0, the equation has more and more multi-bump complex-valued solutions.

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