ON AN INITIAL AND FINAL VALUE PROBLEM FOR FRACTIONAL NONCLASSICAL DIFFUSION EQUATIONS OF KIRCHHOFF TYPE

被引:12
作者
Tuan, Nguyen Huy [1 ,2 ]
机构
[1] Thu Dau Mot Univ, Div Appl Math, Thu Dau Mot, Binh Duong Prov, Vietnam
[2] Univ Sci Ho Chi Minh City VNU, Dept Math & Comp Sci, Ho Chi Minh City, Vietnam
来源
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2021年 / 26卷 / 10期
关键词
pseudo parabolic equation; existence; regularization; Nonlo cal-nonlinear problem; ASYMPTOTIC-BEHAVIOR; NONAUTONOMOUS ATTRACTORS; PARABOLIC EQUATIONS;
D O I
10.3934/dcdsb.2020354
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study for nonlinear Kirchhoff's model of pseudo parabolic type by considering its two different problems. center dot For initial value problem, we obtain the results on the existence and regularity of solutions. Moreover, we also prove that the solutions u corresponding with beta < 1 of the problem convergence to u for beta = 1. center dot For final value problem, we show that the ill-posed property in the sense of Hadamard is occurring. Using the Fourier truncation method to regularize the problem. We establish some stability estimates in the H1 and LP norms under some a-priori conditions on the sought solution.
引用
收藏
页码:5465 / 5494
页数:30
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