Differential and Integral Equations

On blow-up results for solutions of inhomogeneous evolution equations and inequalities. II

A. G. Kartsatos and V. V. Kurta

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Abstract

The main purpose of this work is to further develop ideas and methods from a recent paper by the authors. In particular, we obtain new blow-up results for solutions of the inequality $$ |u|_t \geq \Delta [|u|^\sigma u] + |u|^{q} + \omega (x) $$ on the half-space ${\mathbb R}^1_+ \times {\mathbb R}^n$, where $n\geq 1$, $\sigma\geq 0$, $q>1+\sigma$, and $\omega: {\mathbb R}^n \to {\mathbb R}^1$ is a globally integrable function such that $\int_{{\mathbb R}^n} \omega (x) dx >0$, and establish that for $n>2$ the critical blow-up exponent $q^*=n(1+\sigma)/(n-2)$ is of the blow-up type.

Article information

Source
Differential Integral Equations, Volume 18, Number 12 (2005), 1427-1435.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356059718

Mathematical Reviews number (MathSciNet)
MR2174980

Zentralblatt MATH identifier
1212.35522

Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B40: Asymptotic behavior of solutions 35R45: Partial differential inequalities

Citation

Kartsatos, A. G.; Kurta, V. V. On blow-up results for solutions of inhomogeneous evolution equations and inequalities. II. Differential Integral Equations 18 (2005), no. 12, 1427--1435. https://projecteuclid.org/euclid.die/1356059718


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