On a system of nonlinear pseudoparabolic equations with Robin-Dirichlet boundary conditions

Le Thi Phuong Ngoc; Khong Thi Thao Uyen; Nguyen Huu Nhan; Nguyen Thanh Long

doi:10.3934/cpaa.2021190

Article Contents

2022, Volume 21, Issue 2: 585-623. Doi: 10.3934/cpaa.2021190

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On a system of nonlinear pseudoparabolic equations with Robin-Dirichlet boundary conditions

1.
University of Khanh Hoa, 01 Nguyen Chanh Str., Nha Trang City, Vietnam
2.
Department of Mathematics and Computer Science, University of Science, Vietnam National University Ho Chi Minh City, Eastern International University, Nam Ky Khoi Nghia Str., Hoa Phu Ward, Thu Dau Mot City, Binh Duong Province, Vietnam
3.
Nguyen Tat Thanh University, 300A Nguyen Tat Thanh Str., Dist. 4, Ho Chi Minh City, Vietnam
4.
Department of Mathematics and Computer Science, University of Science, Vietnam National University Ho Chi Minh City, 227 Nguyen Van Cu Str., Dist.5, Ho Chi Minh City, Vietnam

^* Corresponding author
^* Corresponding author

Received: March 31, 2021

Revised: August 31, 2021

Early access: November 2021

Published: February 2022

This research is funded by Vietnam National University HoChiMinh City (VNU-HCM) under grant number B2020-18-01

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Abstract

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.

Keywords:

Nonlinear pseudoparabolic equations,
Faedo-Galerkin method,
local existence,
blow-up,
lifespan,
the global existence and decay of weak solutions.

Mathematics Subject Classification: Primary: 35K70; 35A01; 35B40; 35B44.

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