Differential and Integral Equations

Global existence of positive solutions for semilinear parabolic equations in a half-space

Abstract

We prove the global existence of continuous solutions of the semilinear parabolic problem $\Delta u- {\partial \over {\partial t}}u+ V u^p =0$ in $\mathbb{R}^n_+\times (0,\infty)$, where ${\mathbb{R}^n_+}$ is a half-space in ${\mathbb{R}^n},\, n\geq 3$ . The potential $V$ is in some functional class ${\mathcal K}^{\infty}$. Our approach uses the Shauder fixed-point theorem.

Article information

Source
Differential Integral Equations, Volume 17, Number 11-12 (2004), 1273-1292.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060246

Mathematical Reviews number (MathSciNet)
MR2100027

Zentralblatt MATH identifier
1150.35396

Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35K15: Initial value problems for second-order parabolic equations

Citation

Maatoug, Lamia; Riahi, Lotfi. Global existence of positive solutions for semilinear parabolic equations in a half-space. Differential Integral Equations 17 (2004), no. 11-12, 1273--1292. https://projecteuclid.org/euclid.die/1356060246