# American Institute of Mathematical Sciences

January  2015, 35(1): 399-409. doi: 10.3934/dcds.2015.35.399

## Optimal Liouville-type theorems for a parabolic system

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

Received  September 2013 Revised  June 2014 Published  August 2014

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.
Citation: Quoc Hung Phan. Optimal Liouville-type theorems for a parabolic system. Discrete & Continuous Dynamical Systems - A, 2015, 35 (1) : 399-409. doi: 10.3934/dcds.2015.35.399
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