Disappearance and global existence of interfaces for a doubly degenerate parabolic equation with variable coefficient

作者：Li, Nan; Wang, Liangchen^*; Mu, Chunlai; Zheng, Pan

来源：Mathematical Methods in the Applied Sciences, 2015, 38(8): 1465-1471.

DOI：10.1002/mma.3157

• doubly degenerate parabolic equation
• finite speed of propagation
• variable coefficient
• disappearance of interfaces
• global existence of interfaces

This paper deals with the Cauchy problem for a doubly degenerate parabolic equation with variable coefficient
{u(t) = div (alpha(vertical bar x vertical bar)u(m-1)vertical bar Du vertical bar(lambda-1)Du), x is an element of R-N, t > 0, u(x, 0) = u(0)(x), x is an element of R-N
For the case +1N, one proves that depending on the behavior of the variable coefficient at infinity, the Cauchy problem either possesses the property of finite speed of propagation of perturbation or the support blows up in finite time. This completes a result by Tedeev (A.F.Tedeev, The interface blow-up phenomenon and local estimates for doubly degenerate parabolic equations, Appl. Anal. 86 (2007) 755-782.), which asserts the same result under the condition +1<N.

• 出版日期2015-5-30
• 单位西南财经大学; 重庆大学