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Optimal Liouville-type theorems for a parabolic system

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

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