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2005 On blow-up results for solutions of inhomogeneous evolution equations and inequalities. II
A. G. Kartsatos, V. V. Kurta
Differential Integral Equations 18(12): 1427-1435 (2005).

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.

Citation

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A. G. Kartsatos. V. V. Kurta. "On blow-up results for solutions of inhomogeneous evolution equations and inequalities. II." Differential Integral Equations 18 (12) 1427 - 1435, 2005.

Information

Published: 2005
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35522
MathSciNet: MR2174980

Subjects:
Primary: 35K55
Secondary: 35B40 , 35R45

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.18 • No. 12 • 2005
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