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

Vo Van Au; Yong Zhou; Donal O’Regan

doi:10.1007/s00009-021-01970-8

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

Vo Van Au, Yong Zhou, Donal O’Regan

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

6 Citations (Scopus)

Abstract

In this paper, we consider the Cauchy problem for a semilinear biparabolic equation (∂t+A)2u=G(x,t;u),x∈Ω,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.

Original language	English
Article number	35
Journal	Mediterranean Journal of Mathematics
Volume	19
Issue number	1
DOIs	https://doi.org/10.1007/s00009-021-01970-8
Publication status	Published - Feb 2022

Keywords

biparabolic equation
blow-up
nonlinear problem
Well-posedness

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10.1007/s00009-021-01970-8

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abstract = "In this paper, we consider the Cauchy problem for a semilinear biparabolic equation (∂t+A)2u=G(x,t;u),x∈Ω,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.",

keywords = "biparabolic equation, blow-up, nonlinear problem, Well-posedness",

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AU - Van Au, Vo

AU - Zhou, Yong

AU - O’Regan, Donal

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Y1 - 2022/2

N2 - In this paper, we consider the Cauchy problem for a semilinear biparabolic equation (∂t+A)2u=G(x,t;u),x∈Ω,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.

AB - In this paper, we consider the Cauchy problem for a semilinear biparabolic equation (∂t+A)2u=G(x,t;u),x∈Ω,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.

KW - biparabolic equation

KW - blow-up

KW - nonlinear problem

KW - Well-posedness

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

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Keywords

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