Global existence and asymptotic behavior of solutions to fractional (p,q)-Laplacian equations

Article type: Research Article

Authors: Li, Chunyi | Song, Chaoqun | Quan, LiYan | Xiang, Jianhao | Xiang, Mingqi^{; *}

Affiliations: College of Science, Civil Aviation University of China, Tianjin, 300300, P.R. China

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: The aim of this paper is to consider the following fractional parabolic problem ut+(−Δ)pαu+(−Δ)qβu=f(x,u)(x,t)∈Ω×(0,∞),u=0(x,t)∈(RN∖Ω)×(0,∞),u(x,0)=u0(x)x∈Ω, where Ω⊂RN is a bounded domain with Lipschitz boundary, (−Δ)pα is the fractional p-Laplacian with 0<α<1<p<∞, (−Δ)qβ is the fractional q-Laplacian with 0<β<α<1<q<p<∞, r>1 and λ>0. The global existence of nonnegative solutions is obtained by combining the Galerkin approximations with the potential well theory. Then, by virtue of a differential inequality technique, we give a decay estimate of solutions.

Keywords: Fractional (p, q)-Laplacian, global existence, decay estimates

DOI: 10.3233/ASY-211731

Journal: Asymptotic Analysis, vol. 129, no. 3-4, pp. 321-338, 2022