On the Well-Posedness and Blow-Up for a Semilinear Biparabolic Equation

被引：3

作者：

Vo Van Au ^{[1
,2
]}

Zhou, Yong ^{[3
,4
]}

O'Regan, Donal ^{[5
]}

机构：

[1] Van Lang Univ, Sci & Technol Adv Inst, Div Appl Math, Ho Chi Minh City, Vietnam

[2] Van Lang Univ, Fac Technol, Ho Chi Minh City, Vietnam

[3] Xiangtan Univ, Fac Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

[4] King Abdulaziz Univ, Fac Sci, Nonlinear Anal & Appl Math NAAM Res Grp, Jeddah 21589, Saudi Arabia

[5] Natl Univ Ireland, Sch Math & Stat Sci, Galway, Ireland

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2022年 / 19卷 / 01期

关键词：

Well-posedness; nonlinear problem; biparabolic equation; blow-up; NONLINEAR PARABOLIC EQUATIONS; ASYMPTOTIC-BEHAVIOR; MODEL;

D O I：

10.1007/s00009-021-01970-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the Cauchy problem for a semilinear biparabolic equation (partial derivative t + A)(2)u = G(x,t;u), x is an element of Omega, t >= 0. Results of the local well-posedness (local existence, regularity, and continuous dependence) are given when G is globally Lipschitz. Also, the existence for large times (continuation) of the solutions and a finite time blow-up results are proposed when G is locally Lipschitz functions.

引用

页数：23

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