A nonlinear degenerate parabolic equation
A note on measure-valued solutions to the full Euler system
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.
A semilinear equation in
Addition de variables et application à la régularité
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.
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.
Boundary regularity of solutions of the inhomogeneous Cauchy-Riemann equations
Catastrophes and partial differential equations
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
Diffraction by convex bodies
Doubling properties for second order parabolic equations.
Geometrische Eigenschaften der Lösungen der Differentialgleichung (1-zz)2wzz - n(n + 1) w= 0.
Global Bifurcation of Waves.
Introduction
Large time behavior in a density-dependent population dynamics problem with age structure and child care
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.
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.
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
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) > 0 such that, for 0 < ε < 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.