Optimal Liouville-type theorems for a  parabolic system

Quoc Hung Phan

doi:10.3934/dcds.2015.35.399

Article Contents

2015, Volume 35, Issue 1: 399-409. Doi: 10.3934/dcds.2015.35.399

This issue Previous Article Symplectic groupoids and discrete constrained Lagrangian mechanics Next Article On the $\Gamma$-limit for a non-uniformly bounded sequence of two-phase metric functionals

Optimal Liouville-type theorems for a parabolic system

Quoc Hung Phan^1,

1.
Institute of Research and Development, Duy Tan University, Da Nang

Received: August 31, 2013

Revised: May 31, 2014

Published: December 2014

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Abstract

We prove Liouville-type theorems for a parabolic system in dimension $N=1$ and for radial solutions in all dimensions under an optimal Sobolev growth restriction on the nonlinearities. This seems to be the first example of a Liouville-type theorem in the whole Sobolev subcritical range for a parabolic system (even for radial solutions). Moreover, this also seems to be the first application of the Gidas-Spruck technique to a parabolic system.

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Mathematics Subject Classification: Primary: 35B53, 35B33; Secondary: 35K55.

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