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November/December 2015 Parabolic equations with singular and supercritical reaction terms
Lucio Boccardo, Miguel Escobedo, Maria Michaela Porzio
Differential Integral Equations 28(11/12): 1155-1172 (November/December 2015).

Abstract

We prove that, for every $\lambda \gt 0 $ and $u_0 \geq 0$, the following evolution problem has a solution for small value of $T$, \begin{equation} \label{zbep1} \begin{cases} u > 0 \text{ in }\;\Omega_T = \Omega \times (0,T) \;, \\ \displaystyle \; u_t - \div (M(x)\nabla u)= \frac{\lambda}{u^\gamma}+ \mu \, u^{p} \; \text{ in }\;\Omega_T, \\ u=0 \text{ on }\;\partial\Omega \times (0,T),\\ u(0)=u_0 \text{ in }\; \Omega, \end{cases} \end{equation} where $\gamma > 0$, $\mu\geq0$ and $p > 0$. Moreover, we show the existence of a solution for every value of $T$ for suitable small data $\lambda$ and $u_0$ if $p > 1$ and for every data if $0 < p < 1$.

Citation

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Lucio Boccardo. Miguel Escobedo. Maria Michaela Porzio. "Parabolic equations with singular and supercritical reaction terms." Differential Integral Equations 28 (11/12) 1155 - 1172, November/December 2015.

Information

Published: November/December 2015
First available in Project Euclid: 18 August 2015

zbMATH: 1374.35193
MathSciNet: MR3385138

Subjects:
Primary: 35K10, 35K58, 35K67

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.28 • No. 11/12 • November/December 2015
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