TY - JOUR
T1 - Asymptotically Self-similar Global Solutions for a Higher-order Semilinear Parabolic System
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 - <p>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 &gt; 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.</p>