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Asymptotically self-similar global solutions of a semilinear parabolic equation with a nonlinear gradient term
S. Snoussi, S. Tayachi, F. B. Weissler
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Source: Crossref
Published: Jan 1, 1999
DOI: 10.1017/s0308210500019399
Open original source ↗Source abstract
We study the existence and the asymptotic behaviour of global solutions of the semilinear parabolic equation u(0) = ϧwhere a, b ∈ℝ, q > 1, p > 1. For q = 2p/ ( p +1) and ½ 1(p-1)>1 (equivalently, q > ( n + 2)/( n + 1)), we prove the existence of mild global solutions for small initial data with respect to some norm. Some of those solutions are asymptotically self-similar.
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