Asymptotic behavior for a singular diffusion equation with gradient absorption

作者：Iagar Razvan Gabriel^*; Laurencot Philippe

来源：Journal of Differential Equations, 2014, 256(8): 2739-2777.

DOI：10.1016/j.jde.2014.01.016

• Large time behavior
• Singular diffusion
• Gradient absorption
• Very singular solutions
• p-Laplacian
• Bounded measures

We study the large time behavior of non-negative solutions to the singular diffusion equation with gradient absorption
partial derivative(t)u - Delta(p)u + vertical bar del u vertical bar(q) = 0 in (0,infinity) x R-N,
for p(c) := 2N/(N + 1) < p < 2 and p/2 < q < q(*) := p-N/(N + 1). We prove that there exists a unique very singular solution of the equation, which has self-similar form and we show the convergence of general solutions with suitable initial data towards this unique very singular solution.

• 出版日期2014-4-15