Critical exponent for semilinear damped wave equations in the N-dimensional half space

[摘要] We generalize a previous result of Ikehata (Math. Methods Appl. Sci., in press), which studies the critical exponent problem of a semilinear damped wave equation in the one-dimensional half space, to the general N-dimensional half space case. That is to say, one can show the small data global existence of solutions of a mixed problem for the equation u(tt) - Deltau + u(t) = \u\(p) with the power p satisfying p* (N) = 1 + 2/(N + 1) < p <= N/[N - 2](+) if we deal with the problem in the N-dimensional half space. (C) 2003 Elsevier Inc. All rights reserved.

[发布日期] 2003-12-15

[关键词] similinear damped wave equation;N-D half space;weighted initial data;fast decay;critical exponent