Asymptotically self-similar global solutions for a higher-order semilinear parabolic equation

作者：Sun Fuqin^*; Li Fan; Jia Xiuqing

来源：Mathematical Methods in the Applied Sciences, 2010, 33(12): 1473-1481.

DOI：10.1002/mma.1260

• higher-order parabolic equation
• mild global solutions
• asymptotic self-similar

In this paper, we study the higher-order semilinear parabolic equation
{u(t) (-Delta)(m)u=a vertical bar u vertical bar(p-1)u, (t,x)is an element of R( )(1) x R(N),
u(0,x)=phi(x), x is an element of R(N),
where m, p>1 and a is an element of R. For p>1 2m/N, we prove that the global existence of mild solutions for small initial data with respect to some norm. Some of those solutions are proved to be asymptotic self-similar.

• 出版日期2010-8
• 单位天津职业技术师范大学