| Texto completo | |
| Autor(es): |
Ebert, Marcelo Rempel
;
Marques, Jorge
;
do Nascimento, Wanderley Nunes
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS; v. 31, n. 2, p. 33-pg., 2024-03-01. |
| Resumo | |
In this paper, we derive suitable optimal Lp - Lq decay estimates, 1 < p < 2 < q < oo, for the solutions to the sigma-evolution equation, sigma > 1, with scale -invariant time -dependent damping and power nonlinearity |u|p, utt + (-Delta)sigma u + mu 1 + tut = |u|p, t > 0, x E Rn, where mu > 0, p > 1. The critical exponent p = pc for the global (in time) existence of small data solutions to the Cauchy problem is related to the long time behavior of solutions, which changes accordingly mu E (0, 1) or mu > 1. Under the assumption of small initial data in Lm(Rn) n L2(Rn), m = 1, 2, we find the critical exponent at low space dimension n with respect to sigma, namely, pc = max {p<overline>(gamma m), p<overline>(gamma m + mu - 1)} , gamma m := n , mu > 1 - gamma m, m sigma where p<overline>(gamma) :=1+ 2 gamma is the well known Fujita exponent. Hence, pc = p<overline>(gamma m) if mu > 1, whereas pc = p<overline>(gamma m + mu - 1) is a shift of Fujita type exponent if mu E (0, 1). (AU) | |
| Processo FAPESP: | 20/08276-9 - Método da fase estacionária e aplicações para equações diferenciais parciais de evolução |
| Beneficiário: | Marcelo Rempel Ebert |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |