Differential and Integral Equations

Unbounded solutions to defocusing parabolic systems

Delphine Côte

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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.

Article information

Source
Differential Integral Equations, Volume 28, Number 9/10 (2015), 899-940.

Dates
First available in Project Euclid: 23 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.die/1435064544

Mathematical Reviews number (MathSciNet)
MR3360724

Zentralblatt MATH identifier
1363.35147

Subjects
Primary: 35K15: Initial value problems for second-order parabolic equations 35C15: Integral representations of solutions 35Q56: Ginzburg-Landau equations

Citation

Côte, Delphine. Unbounded solutions to defocusing parabolic systems. Differential Integral Equations 28 (2015), no. 9/10, 899--940. https://projecteuclid.org/euclid.die/1435064544


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