Efficient numerical algorithms for close estimation of critical parameters and quenching times in singular parabolic problems

Mooney, J. W.

doi:10.1016/s0362-546x(97)00361-1

Nonlinear Analysis: Theory, Methods & Applications

1997

DOI: 10.1016/s0362-546x(97)00361-1

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Efficient numerical algorithms for close estimation of critical parameters and quenching times in singular parabolic problems

J. W. Mooney

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2010

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Dynamics of dislocation densities in a bounded channel. Part I: smooth solutions to a singular coupled parabolic system

Ibrahim¹,

Jazar²,

Monneau³

2010

Communications on Pure &Amp; Applied Analysis

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We study a coupled system of two parabolic equations in one space dimension. This system is singular because of the presence of one term with the inverse of the gradient of the solution. Our system describes an approximate model of the dynamics of dislocation densities in a bounded channel submitted to an exterior applied stress. The system of equations is written on a bounded interval with Dirichlet conditions and requires a special attention to the boundary. The proof of existence and uniqueness is done under the use of two main tools: a certain comparison principle on the gradient of the solution, and a parabolic Kozono-Taniuchi inequality.

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Dynamics of dislocation densities in a bounded channel. Part I: smooth solutions to a singular coupled parabolic system

Ibrahim¹,

Jazar²,

Monneau³

2010

Communications on Pure &Amp; Applied Analysis

View full text Add to dashboard Cite

show abstract

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Efficient numerical algorithms for close estimation of critical parameters and quenching times in singular parabolic problems

Cited by 1 publication

References 11 publications

Dynamics of dislocation densities in a bounded channel. Part I: smooth solutions to a singular coupled parabolic system

Dynamics of dislocation densities in a bounded channel. Part I: smooth solutions to a singular coupled parabolic system

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