Tohoku Mathematical Journal
2011
December
SECOND SERIES VOL. 63, NO. 4

Tohoku Math. J.
63 (2011), 561-579

Title HOMOCLINIC AND HETEROCLINIC ORBITS FOR A SEMILINEAR PARABOLIC EQUATION

Author Marek Fila and Eiji Yanagida

(Received December 25, 2009, revised September 17, 2010)
Abstract. We study the existence of connecting orbits for the Fujita equation with a critical or supercritical exponent. For certain ranges of the exponent we prove the existence of heteroclinic connections from positive steady states to zero and a homoclinic orbit with respect to zero.

2000 Mathematics Subject Classification. Primary 35K55; Secondary 35B05, 35B40, 35V05.
Key words and phrases. Homoclinic orbit, heteroclinic orbits, ancient solutions, stationary solutions, self-similar solutions.

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