Thu Dau Mot University Journal of Science


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2 papers


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.
In this paper, we study the Robin-Dirchlet problem (Pn) for a wave equation with the term 1 n Xn i=1 u2( i−1 n , t), n ∈ N. First, for each n ∈ N, under suitable conditions, we prove the local existence and uniqueness of the weak solution un of (Pn). Next, we prove that the sequence of solutions un of (Pn) converges strongly in appropriate spaces to the weak solution u of the problem (P), where (P) is defined by (Pn) by replacing 1 n Xn i=1 u2( i−1 n , t) by Z 1 0 u2(y, t)dy. The main tools used here are the linearization method together with the Faedo-Galerkin method and the weak compact method. We end the paper with a remark related to a similar problem.

Publication Information

Publisher

Thu Dau Mot University, Viet Nam

Honorary Editor-in-Chief and Chairman of the Editorial Board

Assoc. Prof. Nguyen Van Hiep

Deputy Editor-in-Chief

PhD. Trần Hạnh Minh Phương
Thu Dau Mot University

Editorial Board

Prof. Tran Van Doan
Fujen University, Taiwan
Prof. Zafar Uddin Ahmed
Vietnam National University Ho Chi Minh City

Prof.Dr. Phillip G.Cerny
The University of Manchester, United Kingdom
Prof. Ngo Van Le
University of Social Sciences and Humanities (VNU-HCM)

Prof. Bui The Cuong
Southern Institute of Social Sciences​​​​​​​
Prof. Le Quang Tri
Can Tho University

Assoc. Prof. Nguyen Van Duc
Animal Husbandry Association of Vietnam
Assoc. Prof. Ted Yuchung Liu
National Pingtung University, Taiwan

PhD. Anita Doraisami
Economics Monash University, Australia
Prof. Dr. Andrew Seddon
Asia Pacific University of Technology & innovation (APU)

Assoc. Prof. Le Tuan Anh
Thu Dau Mot University
Prof. Abtar Darshan Singh
Asia Pacific University, Malaysia

Prof.Dr. Ron W.Edwards
The University of Melbourne, Australia
Assoc. Prof. Hoang Xuan Nien
Thu Dau Mot University

PhD. Nguyen Duc Nghia
Vietnam National University Ho Chi Minh City
PhD. Bao Dat
Monash University (Australia)

PhD. Raqib Chowdhury
Monash University (Australia)
PhD. Nguyen Hoang Tuan
Thu Dau Mot University

PhD. Nguyen Thi Lien Thuong
Thu Dau Mot University

Assistant

Nguyen Thi Man
Thu Dau Mot University