General decay and lifespan of solutions for a system of nonlinear pseudoparabolic equations with viscoelastic term

By Khong Thi Thao Uyen, Nguyen Anh Triet, Le Thi Phuong Ngoc
DOI: 10.37550/tdmu.EJS/2023.05.415

In this paper, we consider the Robin-Dirichlet problem for a system of nonlinear pseudoparabolic
equations with viscoelastic term. By the Faedo-Galerkin method, we first prove
the existence and uniqueness of solution for the problem. Next, we give a sufficient condition
to get the global existence and decay of the weak solution. Finally, by the concavity method,
we prove the blow-up result of the solution when the initial energy is negative. Furthermore,
we establish here the lifespan of the solution by finding the upper bound and the lower bound
for the blow-up time.