2008
DOI: 10.1002/mma.1089
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Existence of solutions to a phase transition model with microscopic movements

Abstract: SUMMARYWe prove the existence of weak solutions for a 3D phase change model introduced by Michel Frémond in (Non-smooth Thermomechanics. Springer: Berlin, 2002) showing, via a priori estimates, the weak sequential stability property in the sense already used by the first author in (Comput. Math. Appl. 2007; 53:461-490). The result follows by passing to the limit in an approximate problem obtained adding a superlinear part (in terms of the gradient of the temperature) in the heat flux law. We first prove well … Show more

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Cited by 37 publications
(58 citation statements)
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“…In [RR15], under a weaker growth condition on K than the present (2.6), it was possible to prove an existence result for a weaker formulation of (2.17), consisting of an entropy inequality and of a total energy inequality. The resulting notion of "entropic" solution, originally proposed in [FPR09], indeed reflects the strict positivity of the temperature, and the fact that the entropy increases along solutions. Without going into details, let us mention that this entropy inequality is (formally) obtained by testing (2.17) by ϕ θ −1 , with ϕ a smooth test function, and integrating in time.…”
Section: Weak Formulation and Main Existence Resultsmentioning
confidence: 72%
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“…In [RR15], under a weaker growth condition on K than the present (2.6), it was possible to prove an existence result for a weaker formulation of (2.17), consisting of an entropy inequality and of a total energy inequality. The resulting notion of "entropic" solution, originally proposed in [FPR09], indeed reflects the strict positivity of the temperature, and the fact that the entropy increases along solutions. Without going into details, let us mention that this entropy inequality is (formally) obtained by testing (2.17) by ϕ θ −1 , with ϕ a smooth test function, and integrating in time.…”
Section: Weak Formulation and Main Existence Resultsmentioning
confidence: 72%
“…The techniques from [FPR09] have been recently extended in [RR15] to analyze a model for ratedependent damage in thermo-viscoelasticity. Namely, in place of the 1 -homogeneous dissipation potential R 1 from (1.2), the flow rule for the damage parameter in [RR15] features the quadratic dissipation…”
Section: Weak Formulation and Main Existence Resultsmentioning
confidence: 99%
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“…When nonlinear heat flux q = −k 0 θ∇θ is considered (see, for example, [1,14]), our method can be also applied in the long-time behaviour analysis with some modification. When nonlinear heat flux q = −k 0 θ∇θ is considered (see, for example, [1,14]), our method can be also applied in the long-time behaviour analysis with some modification.…”
Section: J Jiangmentioning
confidence: 99%