On a Robin-Dirichlet problem for a system of nonlinear pseudoparabolic equations
with the viscoelastic term
Khong Thi Thao Uyen, Nguyen Anh Triet, Le Thi Phuong Ngoc, Nguyen Thanh Long
Received May 26, 2024. Published online February 21, 2025.
Abstract: 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.
Keywords: nonlinear pseudoparabolic equation; Faedo-Galerkin method; local existence; blow-up; lifespan; the global existence and decay of weak solutions
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Affiliations: Khong Thi Thao Uyen, Faculty of Mathematics and Computer Science, University of Science, Vietnam National University Ho Chi Minh City, F09, 227 Nguyen Van Cu, District 5, Ho Chi Minh City, Vietnam; Eastern International University, Nam Ky Khoi Nghia Street, Hoa Phu Ward, Thu Dau Mot City, Binh Duong Province, Vietnam, e-mail: uyen.khong@eiu.edu.vn; Nguyen Anh Triet, University of Architecture Ho Chi Minh City, 196 Pasteur, Vo Thi Sau Ward, District 3, Ho Chi Minh City, Vietnam, e-mail: triet.nguyenanh@uah.edu.vn; Le Thi Phuong Ngoc, University of Khanh Hoa, 01 Nguyen Chanh Str., Nha Trang City, Vietnam, e-mail: ngoc1966@gmail.com; Nguyen Thanh Long (corresponding author), Faculty of Mathematics and Computer Science, University of Science, Vietnam National University Ho Chi Minh City, F09, 227 Nguyen Van Cu, District 5, Ho Chi Minh City, Vietnam, e-mail: longnt2@gmail.com
