The influence of data regularity in the critical exponent for a class of semilinear evolution equations

Autor(es)

Ebert, Marcelo R. ^[1] ; da Luz, Cleverson R. ^[2] ; Palma, Maira F. G. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Dept Comp & Math, BR-14040901 Ribeirao Preto, SP - Brazil

^[2] Univ Fed Santa Catarina, Dept Math, Campus Trindade, BR-88040900 Florianopolis, SC - Brazil

• Tipo de documento: Artigo Científico
• Fonte: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS; v. 27, n. 5 JUL 27 2020.
• Citações Web of Science: 0

Resumo

In this paper we find the critical exponent for the global existence (in time) of small data solutions to the Cauchy problem for the semilinear dissipative evolution equations u(tt) + (-Delta)(delta) u(tt) + (-Delta)(alpha)u + (-Delta)(theta) u(t) = vertical bar ut vertical bar(p), t >= 0, x is an element of R-n, with p > 1, 2 theta is an element of {[}0, alpha] and delta is an element of (theta, alpha]. We show that, under additional regularity (H alpha+delta (R-n) boolean AND L-m (R-n)) x (H-2 delta (R-n) boolean AND L-m (R-n)) for initial data, with m is an element of (1, 2], the critical exponent is given by p(c) = 1+ 2m theta/n. The nonexistence of global solutions in the subcritical cases is proved, in the case of integers parameters alpha, delta, theta, by using the test function method (under suitable sign assumptions on the initial data). (AU)

• Processo FAPESP: 17/19497-3 - Comportamento assintótico de soluções para uma classe de equações diferenciais parciais de difusão e aplicações
• Beneficiário: Marcelo Rempel Ebert
• Linha de fomento: Auxílio à Pesquisa - Regular