# The nonlinear heat equation via fixed point principles

## Abstract

Starting with the existence and uniqueness result of J.L.Lions for the non-homogenous heat equation with the source term in $$H^{-1}\left(\Omega \right)$$, we ppresent existence results for the nonlinear perturbed heat equation via Banach, Schauder and Leray-Schauder principles.

## Authors

Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

## Keywords

Parabolic equation; Nonlinear operator; Sobolev space.

## Paper coordinates

R. Precup, The nonlinear heat equation via fixed point principles,  Annals of the Tiberiu Popoviciu Seminar 4 (2006), 111-127.

## PDF

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##### Journal

Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity

1584-4536