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Volume 22, Issue 3
Asymptotically Self-similar Global Solutions for a Higher-order Semilinear Parabolic System

Fuqin Sun , Fan Li & Xiuqing Jia

DOI: 10.4208/jpde.v22.n3.6

J. Part. Diff. Eq., 22 (2009), pp. 282-298.

Published online: 2009-08

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  • 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.

  • Keywords

Higher-order parabolic equation mild global solutions asymptotically self-similar

  • AMS Subject Headings

35K55 35K65

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-22-282, author = {Fuqin Sun , Fan Li and Xiuqing Jia }, title = {Asymptotically Self-similar Global Solutions for a Higher-order Semilinear Parabolic System}, journal = {Journal of Partial Differential Equations}, year = {2009}, volume = {22}, number = {3}, pages = {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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v22.n3.6}, url = {http://global-sci.org/intro/article_detail/jpde/5258.html} }
TY - JOUR T1 - Asymptotically Self-similar Global Solutions for a Higher-order Semilinear Parabolic System AU - Fuqin Sun , Fan Li & Xiuqing Jia JO - Journal of Partial Differential Equations VL - 3 SP - 282 EP - 298 PY - 2009 DA - 2009/08 SN - 22 DO - http://doi.org/10.4208/jpde.v22.n3.6 UR - https://global-sci.org/intro/article_detail/jpde/5258.html KW - Higher-order parabolic equation KW - mild global solutions KW - asymptotically self-similar AB -

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.

Fuqin Sun , Fan Li and Xiuqing Jia . (2009). Asymptotically Self-similar Global Solutions for a Higher-order Semilinear Parabolic System. Journal of Partial Differential Equations. 22 (3). 282-298. doi:10.4208/jpde.v22.n3.6
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