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Article

Uyen, Khong Thi Thao ; Triet, Nguyen Anh ; Ngoc, Le Thi Phuong ; Long, Nguyen Thanh
On a Robin-Dirichlet problem for a system of nonlinear pseudoparabolic equations with the viscoelastic term. (English). Mathematica Bohemica, vol. 151 (2026), issue 1, pp. 105-152
MSC: 35A01, 35B40, 35B44, 35K70 | DOI: 10.21136/MB.2025.0059-24
Keywords:
nonlinear pseudoparabolic equation; Faedo-Galerkin method; local existence; blow-up; lifespan; the global existence and decay of weak solutions
Summary:
We consider a Robin-Dirichlet problem for a system of nonlinear pseudoparabolic equations with the viscoelastic term. Based on the Faedo-Galerkin method, we first prove existence and uniqueness. Next, we give a sufficient condition for the global existence and decay of weak solutions. Finally, using concavity method, we prove blow-up results for solutions when the initial energy is nonnegative or negative. Furthermore, we establish here the lifespan for the equation via finding the upper bound and the lower bound for the blow-up times.
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