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September/October 2015 Unbounded solutions to defocusing parabolic systems
Delphine Côte
Differential Integral Equations 28(9/10): 899-940 (September/October 2015).

Abstract

We give existence theorems for the Cauchy problem of a large class of semi-linear parabolic equations in $L^{\infty}$, $L^{\infty} \cap L^p$ or $L^{\infty} \cap \dot W^{1,p}$, using a contracting map argument. We then construct integral solutions to parabolic equations with data growing at infinity and defocusing nonlinearity, and give an example of instantaneous blow up when the nonlinearity is focusing and the initial data has tame growth.

Citation

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Delphine Côte. "Unbounded solutions to defocusing parabolic systems." Differential Integral Equations 28 (9/10) 899 - 940, September/October 2015.

Information

Published: September/October 2015
First available in Project Euclid: 23 June 2015

zbMATH: 1363.35147
MathSciNet: MR3360724

Subjects:
Primary: 35C15, 35K15, 35Q56

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.28 • No. 9/10 • September/October 2015
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