Quenching for a reaction–diffusion system with logarithmic singularity

Mu, Chunlai; Zhou, Shouming; Liu, Dengming

doi:10.1016/j.na.2009.04.055

Cited by 12 publications

(8 citation statements)

References 14 publications

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“…Therefore, we extend the corresponding results of [14,16,18] to a more general system (1.1) in this paper.…”

Section: Introduction and Main Resultssupporting

confidence: 56%

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Quenching for a parabolic system with general singular terms

Pei¹,

Li²

2016

J. Nonlinear Sci. Appl.

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In this paper, we study a parabolic system with general singular terms and positive Dirichlet boundary conditions. Some sufficient conditions for finite-time quenching and global existence of the solutions are obtained, and the blow-up of time-derivatives at the quenching point is verified. Furthermore, under some appropriate hypotheses, we prove that the quenching point is only origin and quenching of the system is non-simultaneous. Moreover, the estimate of quenching rate of the corresponding solution is established in this article.

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“…Therefore, we extend the corresponding results of [14,16,18] to a more general system (1.1) in this paper.…”

Section: Introduction and Main Resultssupporting

confidence: 56%

“…Afterwards, Mu et al in [14] studied the following reaction-diffusion system with logarithmic singularity,…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Quenching for a parabolic system with general singular terms

Pei¹,

Li²

2016

J. Nonlinear Sci. Appl.

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“…Motivated by those papers and references therein, the main purpose of this paper is to study a more general system (1) to obtain a lot of more general conclusions for the non-simultaneous quenching phenomenon with coupled fluxes at the boundary, which appeared in many papers with some special case, see [2][3][4][5][6][11][12][13].…”

Section: T V T T T P Q P Q U T T T V T T T P Q U T T T V T T T Q Pmentioning

confidence: 99%

Quenching for a Diffusion System with Coupled Boundary Fluxes

Pei

Zhao

2016

ACM

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Abstract:In this paper, we investigate a diffusion system of two parabolic equations with more general singular coupled boundary fluxes. Within proper conditions, we prove that the finite quenching phenomenon happens to the system. And we also obtain that the quenching is non-simultaneous and the corresponding quenching rate of solutions. This extends the original work by previous authors for a heat system with coupled boundary fluxes subject to non-homogeneous Neumann boundary conditions.

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“…There are many papers considering the quenching phenomenon for the solutions of parabolic systems ( [3], [9], [10]). …”

Section: Introductionmentioning

confidence: 99%

Quenching problems for a semilinear reaction-diffusion system with singular boundary outflux

Selçuk¹

2016

Tamkang J. Math.

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Abstract.In this paper, we study two quenching problems for the following semilinear reaction-diffusion system:where p 1 , p 2 , q 1 , q 2 are positive constants and u 0 (x), v 0 (x) are positive smooth functions. We firstly get a local exisence result for this system. In the first problem, we show that quenching occurs in finite time, the only quenching point is x = 0 and (u t , v t ) blows up at the quenching time under the certain conditions. In the second problem, we show that quenching occurs in finite time, the only quenching point is x = 1 and (u t , v t ) blows up at the quenching time under the certain conditions.

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Quenching for a reaction–diffusion system with logarithmic singularity

Cited by 12 publications

References 14 publications

Quenching for a parabolic system with general singular terms

Quenching for a parabolic system with general singular terms

Quenching for a Diffusion System with Coupled Boundary Fluxes

Quenching problems for a semilinear reaction-diffusion system with singular boundary outflux

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