TY - JOUR
T1 - Self-similar Singular Solution of a P-Laplacian Evolution Equation with Gradient Absorption Term
JO - Journal of Partial Differential Equations
VL - 4
SP - 369
EP - 383
PY - 2004
DA - 2004/11
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5399.html
KW - p-Laplacian evolution equation
KW - gradient absorption
KW - self-similar
KW - singular solution
KW - very singular solution
AB - <p>In this paper we deal with the self-similar singular solution of the p-Laplacian evolution equation u_t = div(|∇|^{p-2}∇u) - |∇u|^q for p &gt; 2 and q &gt; 1 in R^n × (0, ∞). We prove that when p &gt; q + n/(n + 1) there exist self-similar singular solutions, while p ≤ q+n/(n+1) there is no any self-similar singular solution. In case of existence, the self-similar singular solutions are the self-similar very singular solutions, which have compact support. Moreover, the interface relation is obtained.</p>