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General decay for a nonlinear pseudo-parabolic equation with viscoelastic term

Vu Ngo Tran, Dung Dao Bao, Dung Huynh Thi Hoang

Demonstratio Mathematica

2022

Vol. 55, nr 1

737--751

This work is concerned with a multi-dimensional viscoelastic pseudo-parabolic equation with critical Sobolev exponent. First, with some suitable conditions, we prove that the weak solution exists globally. Next, we show that the stability of the system holds for a much larger class of kernels than the ones considered in previous literature. More precisely, we consider the kernel g:[0,∞)⟶(0,∞) satisfying g′(t)⩽−ξ(t)G(g(t)) , where ξ and G are functions satisfying some specific properties.