Showing papers in "Indiana University Mathematics Journal in 1986"

A general variational identity

Abstract: Etablissement d'une identite relative aux extremales du probleme variationnel general, analogue a celle de Pohozaev pour les solutions du probleme de Dirichlet Demonstration de la non-existence d'extremales non triviales dans un domaine en etoile

Estimates for the heat kernel for a sum of squares of vector fields

Abstract: On trouve des bornes inferieures et superieures au noyau de la chaleur pour une somme de carres de champs vectoriels

Bubble growth in porous media

Abstract: Etude de la croissance des bulles en milieu poreux par la resolution d'une equation aux derivees partielles avec des conditions appropriees

A description of blow-up for the solid fuel ignition model

Abstract: Friedman and McLeod [4] recently proved that blow-up occurs only at the origin x = 0 and in addition that u(x,t) satisfies the fol2 £nlx I + c for all ~ 0 such that ut(x,t) h R R @e u(x't) t £ [~ T) x E [-~, ~] ; and iv) -£n(T-t) < u(0,t) < , u r -_

Pointwise A-Priori Bounds for Strongly Coupled Semilinear Parabolic Systems.

Abstract: : The prototype parabolic partial differential equation is the heat conduction equation. This paper deals with systems of parabolic equations. Such systems occur in many contexts in addition to heat conduction, e.g. biology, in nuclear reactor techniques, in economics, etc. Let the n-vector u denote the (unknown) solution of a system of n parabolic partial differential equations. An important question in the study of these systems is the boundedness of u. Many techniques and criteria have been developed to solve this problem if the system is weakly coupled, i.e. if the k sub th equation contains second order space derivatives of only u sub k, the k sub th component of u. If this is not the case, the system is said to be strongly coupled. This paper for a broad class of strongly coupled parabolic systems pointwis boundedness of the solution u is established.

A weighted inequality and eigenvalue estimates for Schrödinger operators

Abstract: On presente des estimations des operateurs de Schrodinger de la forme H=−Π-v+w, ou v,w≥0 sur R n , n≥3

First order partial differential equations with singular solution

Abstract: On caracterise intrinsequement cette classe d'equations aux derivees partielles pour demontrer un theoreme d'existence et d'unicite rigoureux pour des solutions et pour montrer comment des invariants de geometrie differentielle associes a l'equation determinent des proprietes des solutions

On the Dirichlet problem with L2 boundary values in a half-space

Abstract: Etude du probleme de Dirichlet avec des donnees aux limites L 2 pour un operateur lineaire uniformement elliptique du second ordre a structure de divergence dans un demi-espace. Application d'une methode d'inegalite d'energie

Exceptional boundary sets for solutions of elliptic partial differential inequalities

Abstract: Etude des ensembles-frontieres exceptionnelles pour les solutions d'inequations aux derivees partielles elliptiques. Generalisation des principes de Phragmen-Lindelof

Factorization of nonnegative operators along commuting sets of projections

Abstract: On presente de nouvelles conditions suffisantes pour qu'une factorisation le long d'une chaine soit aussi une factorisation le long d'un second ensemble de projections qui commute avec la chaine

Holomorphic sections of a homogeneous line bundle associated to an infinite-dimensional Lie group

Abstract: On considere un certain type de structure analytique sur une variete de Banach particuliere