Global solutions and self-similar solutions of semilinear parabolic equations with nonlinear gradient terms

作者：Zhang Qingshan^*; Shi Peihu

来源：Nonlinear Analysis-Theory Methods & Applications, 2010, 72(6): 2744-2752.

DOI：10.1016/j.na.2009.11.020

• Semilinear parabolic equation
• Cauchy problem
• Self-similar solution
• Asymptotically self-similar solution

In this paper we consider the Cauchy problem of semilinear parabolic equations with nonlinear gradient terms a(x)vertical bar u vertical bar(q-1)u vertical bar del u vertical bar(p). We prove the existence of global solutions and self-similar solutions for small initial data. Moreover, for a class of initial data we show that the global solutions behave asymptotically like self-similar solutions as t -> infinity.

• 出版日期2010-3-15
• 单位东南大学