Capacitary estimates of solutions of semilinear parabolic equations |
| |
Authors: | Moshe Marcus Laurent Veron |
| |
Affiliation: | 1. Department of Mathematics, Technion, Haifa, Israel 2. Department of Mathematics, University of Tours, Tours, France
|
| |
Abstract: | We prove that any positive solution of ${partial_tu-Delta u+u^q=0 (q > 1)}$ in ${mathbb{R}^N times (0, infty)}$ with initial trace (F, 0), where F is a closed subset of ${mathbb{R}^{N}}$ can be represented, up to two universal multiplicative constants, by a series involving the Bessel capacity ${C_{2/q, q^{prime}}}$ . As a consequence we prove that there exists a unique positive solution of the equation with such an initial trace. We also characterize the blow-up set of u(x, t) when ${t downarrow 0}$ , by using the “density” of F expressed in terms of the ${C_{2/q, q^{prime}}}$ -Bessel capacity. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|