Year: 2009
Journal of Partial Differential Equations, Vol. 22 (2009), Iss. 3 : pp. 282–298
Abstract
In this paper, we study the higher-order semilinear parabolic system u_t+(-Δ)^mu=a|v|^{p-1}v, t(x)∈R^1_+×R^N, v_t+(-Δ)^mv=b|u|^{q-1}u, t(x)∈R^1_+×R^N, u(0,x)=φ(x), v(0,x)=ψ(x), x∈R^N, where m, p, q > 1, a,b∈R. We prove that the global existence of mild solutions for small initial data with respect to certain norms. Some of these solutions are proved to be asymptotically self-similar.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v22.n3.6
Journal of Partial Differential Equations, Vol. 22 (2009), Iss. 3 : pp. 282–298
Published online: 2009-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Higher-order parabolic equation
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