Le Thi Phuong Ngoc, Dao Thi Hai Yen, Nguyen Thanh Long
This article concerns the initial-boundary value problem for nonlinear pseudo-parabolic equation
where f, , , are given functions. Using the Faedo-Galerkin method and the compactness method, we prove that there exists a unique weak solution u such that , and , . Also we prove that the problem has a unique global solution with -norm decaying exponentially as . Finally, we establish the existence and uniqueness of a weak solution of the problem associated with a periodic condition.
Submitted January 27, 2017. Published January 4, 2018.
Math Subject Classifications: 34B60, 35K55, 35Q72, 80A30.
Key Words: Nonlinear pseudoparabolic equation; asymptotic behavior; exponential decay; periodic weak solution; Faedo-Galerkin method.
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| Le Thi Phuong Ngoc |
University of Khanh Hoa
01 Nguyen Chanh Str., Nha Trang City, Vietnam
| Dao Thi Hai Yen |
Department of Natural Science
Phu Yen University
18 Tran Phu Str., Ward 7, Tuy Hoa City, Vietnam
| Nguyen Thanh Long |
Department of Mathematics and Computer Science
VNUHCM - University of Science
227 Nguyen Van Cu Str., Dist. 5, HoChiMinh City, Vietnam
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