Displaying similar documents to “Stability for approximation methods of the one-dimensional Kobayashi-Warren-Carter system”

On quasistatic inelastic models of gradient type with convex composite constitutive equations

Krzysztof Chełmiński (2003)

Open Mathematics

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This article defines and presents the mathematical analysis of a new class of models from the theory of inelastic deformations of metals. This new class, containing so called convex composite models, enlarges the class containing monotone models of gradient type defined in [1]. This paper starts to establish the existence theory for models from this new class; we restrict our investigations to the coercive and linear self-controlling case.

Existence and approximation results for gradient flows

Riccarda Rossi, Giuseppe Savaré (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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This note addresses the Cauchy problem for the gradient flow equation in a Hilbert space H u ' ( t ) + ∂ φ ( u ( t ) ) ∋ 0 a.e. in ( 0 , T ) , u ( 0 ) = u 0 , where φ : H → ( - ∞ , + ∞ ] is a proper, lower semicontinuous functional which is not supposed to be a (smooth perturbation of a) convex functional and ∂ φ is (a suitable limiting version of) its subdifferential. The interest for this kind of equations is motivated by a number of examples, which show that several mathematical models describing phase transitions phenomena and leading to systems of evolutionary...

Best simultaneous L p approximations

Yusuf Karakuş (1998)

Czechoslovak Mathematical Journal

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In this paper we study simultaneous approximation of n real-valued functions in L p [ a , b ] and give a generalization of some related results.

Non-local approximation of free-discontinuity problems with linear growth

Luca Lussardi, Enrico Vitali (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We approximate, in the sense of -convergence, free-discontinuity functionals with linear growth in the gradient by a sequence of non-local integral functionals depending on the average of the gradients on small balls. The result extends to higher dimension what we already proved in the one-dimensional case.