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
