Initial Boundary Value Problems for a Class of Non-linear Pseudo-parabolic Equation

Chinese Quarterly Journal of Mathematics ›› 2010, Vol. 25 ›› Issue (3): 335-343.

Initial Boundary Value Problems for a Class of Non-linear Pseudo-parabolic Equation

1. Department of Mathematics, Zhengzhou University2. Department of Mathematics and Information Science, Henan University of Urban Construction

Received:2007-03-27 Online:2010-09-30 Published:2023-05-24
About author: GUO Hong-xia(1978- ), female, native of Linzhou, Henan, Ph.D., a lecturer of Zhengzhou University, engages in nonlinear evolution equation; HAN Xian-jun(1973- ), male, native of Yanshi, Henan, Ph.D., a lecturer of Henan University of Urban Construction, engages in nonlinear evolution equation.
Supported by:
Supported by the National Natural Science Foundation of China(10671182)；

Abstract

Abstract: In this paper, the existence, the uniqueness, the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation u_t-αu_xx-βu_xxt=F(u)-βF (u)_xx are proved, where α, β > 0 are constants, F(s) is a given function.

Key words: non-linear pseudo-parabolic equation, initial boundary problem, global existence and uniqueness of solutions, asymptotic behavior, non-existence

CLC Number:

O175.26

GUO Hong-xia, HAN Xian-jun. Initial Boundary Value Problems for a Class of Non-linear Pseudo-parabolic Equation [J]. Chinese Quarterly Journal of Mathematics, 2010, 25(3): 335-343.

[1]	LI Jiao-long, QIN Yu-ming. Global Existence, Asympotic Behavior and Uniform Attractors for Thermoelastic Systems [J]. Chinese Quarterly Journal of Mathematics, 2017, 32(3): 221-237.
[2]	ZHENG Xiu-zhen. Global Existence, Asymptotic Behavior and Uniform Attractors of Timoshenko Systems with Gurtin-Pipkin Thermal Law [J]. Chinese Quarterly Journal of Mathematics, 2016, 31(3): 307-330.
[3]	CAO Jie. Global Existence, Asymptotic Behavior and Uniform Attractors for a Third Order in Time Dynamics [J]. Chinese Quarterly Journal of Mathematics, 2016, 31(3): 221-236.
[4]	SHI Qi-hong, SU Xing, YUAN Guo-qiang, XIAO Qian. Characters of the Solutions to a Generalized Nonlinear Max-type Diﬀerence Equation [J]. Chinese Quarterly Journal of Mathematics, 2013, 28(2): 284-289.
[5]	WANG Bo, WANG Qiang. A Finite Volume Backward Euler Difference Method for Nonlinear Parabolic Integral-differential Equation [J]. Chinese Quarterly Journal of Mathematics, 2009, 24(3): 370-377.
[6]	HAN Xiang-lin. The Asymptotic Behavior for a Nonlinear Singularly Perturbed System [J]. Chinese Quarterly Journal of Mathematics, 2007, 22(2): 175-178.
[7]	CHEN Shou-xin, HAN Xiao-sen . Asymptotic Behavior of Global Smooth Solution of 1-D Quasineutral Drift Diffusion Model for Semiconductors [J]. Chinese Quarterly Journal of Mathematics, 2006, 21(3): 385-396.
[8]	YAN Shu-xia, WANG Zhi-juna. Asymptotic of the Solutions of the Initial Boundary Value Problem for the Diffusion Equations for Semiconductors (Ⅱ) [J]. Chinese Quarterly Journal of Mathematics, 2005, 20(3): 319-325.
[9]	WANG Wen-bin, LIU Shu-mei . Asymptotic of the Solutions to the Initial Boundary Value Problem for the Diffusion Equations for Semiconductors [J]. Chinese Quarterly Journal of Mathematics, 2005, 20(2): 185-191.
[10]	HAN Xiang-lin. The Interior Layer Problem for the Strongly Nonlinear Singularly Perturbed System [J]. Chinese Quarterly Journal of Mathematics, 2004, 19(4): 436-440.
[11]	XU Zhi-ting, XIA Yong. On the Asymptotic Behavior of Certain Second Order Differential Equations [J]. Chinese Quarterly Journal of Mathematics, 2004, 19(2): 186-187.
[12]	Luo Jiaowan, Hou Zhenting, He Chuntian. Asymptotic Behavior of Oscillatory Solutions of Forced Nonlinear Neutral Delay Differential Equations [J]. Chinese Quarterly Journal of Mathematics, 1998, 13(2): 31-35.
[13]	Qi Jiangang, Liu Yansheng. Asymptotic Behavior of Nodal Solutions for Semilinear Elliptic Equationsin Rⁿ [J]. Chinese Quarterly Journal of Mathematics, 1998, 13(1): 22-28.

Initial Boundary Value Problems for a Class of Non-linear Pseudo-parabolic Equation

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 13

Recommended Articles

Metrics

Comments