Open AccessOn a system of nonlinear pseudoparabolic equations with Robin-Dirichlet boundary conditions
Author(s) -
Le Thı Phuong Ngoc,
Khong Thi Thao Uyen,
Nguyễn Hữu Nhẫn,
Nguyễn Thành Long
Publication year - 2022
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021190
Subject(s) - uniqueness , mathematics , dirichlet boundary condition , nonlinear system , upper and lower bounds , mathematical analysis , geodetic datum , dirichlet problem , galerkin method , weak solution , boundary value problem , physics , cartography , quantum mechanics , geography
In this paper, we investigate a system of pseudoparabolic equations with Robin-Dirichlet conditions. First, the local existence and uniqueness of a weak solution are established by applying the Faedo-Galerkin method. Next, for suitable initial datum, we obtain 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, then we establish here the lifespan for the equations via finding the upper bound and the lower bound for the blow-up times.