We consider weak entropy measure-valued soluti ons of the Neumann initial-boundary value problem for the equation ut = [ø(u)]xx, where ø is nonmonotone. These solutions are obtained from the corresponding problem for the regularized equation ut = [ø(u)]xx + euxxt (∈ > 0) by a vanishing viscosity method and satisfy a family of suitable entropy inequalities. Relying on a strong version of these inequalities, we prove exhaustive results concerning the long-time behavior of solutions. © 2010 Societ y for Industrial and Applied Mathematics.

Long-time behavior of solutions to a class of forward-backward parabolic equations / Smarrazzo, Flavia; Tesei, Alberto. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 42:3(2010), pp. 1046-1093. [10.1137/090763561]

Long-time behavior of solutions to a class of forward-backward parabolic equations

SMARRAZZO, FLAVIA;TESEI, Alberto
2010

Abstract

We consider weak entropy measure-valued soluti ons of the Neumann initial-boundary value problem for the equation ut = [ø(u)]xx, where ø is nonmonotone. These solutions are obtained from the corresponding problem for the regularized equation ut = [ø(u)]xx + euxxt (∈ > 0) by a vanishing viscosity method and satisfy a family of suitable entropy inequalities. Relying on a strong version of these inequalities, we prove exhaustive results concerning the long-time behavior of solutions. © 2010 Societ y for Industrial and Applied Mathematics.
2010
entropy inequalities; forward-backward parabolic equations; long-time behavior of solutions; regularization; steady states; young measures
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Long-time behavior of solutions to a class of forward-backward parabolic equations / Smarrazzo, Flavia; Tesei, Alberto. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 42:3(2010), pp. 1046-1093. [10.1137/090763561]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/4009
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