Displaying similar documents to “Some regularizing methods for transport equations and the regularity of solutions to scalar conservation laws”

Regularity in kinetic formulations via averaging lemmas

Pierre-Emmanuel Jabin, Benoît Perthame (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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We present a new class of averaging lemmas directly motivated by the question of regularity for different nonlinear equations or variational problems which admit a kinetic formulation. In particular they improve the known regularity for systems like γ = 3 in isentropic gas dynamics or in some variational problems arising in thin micromagnetic films. They also allow to obtain directly the best known regularizing effect in multidimensional scalar conservation laws. The new ingredient here...

Convergence of implicit Finite Volume methods for scalar conservation laws with discontinuous flux function

Sébastien Martin, Julien Vovelle (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper deals with the problem of numerical approximation in the Cauchy-Dirichlet problem for a scalar conservation law with a flux function having finitely many discontinuities. The well-posedness of this problem was proved by Carrillo [  (2003) 687–705]. Classical numerical methods do not allow us to compute a numerical solution (due to the lack of regularity of the flux). Therefore, we propose an implicit Finite Volume method based on an equivalent formulation of the initial problem....

Regularity of optimal shapes for the Dirichlet’s energy with volume constraint

Tanguy Briancon (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we prove some regularity results for the boundary of an open subset of ℝ d which minimizes the Dirichlet’s energy among all open subsets with prescribed volume. In particular we show that, when the volume constraint is “saturated”, the reduced boundary of the optimal shape (and even the whole boundary in dimension 2) is regular if the state function is nonnegative.

Propagation of Gevrey regularity over long times for the fully discrete Lie Trotter splitting scheme applied to the linear Schrödinger equation

François Castella, Guillaume Dujardin (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, we study the linear Schrödinger equation over the -dimensional torus, with small values of the perturbing potential. We consider numerical approximations of the associated solutions obtained by a symplectic splitting method (to discretize the time variable) in combination with the Fast Fourier Transform algorithm (to discretize the space variable). In this fully discrete setting, we prove that the regularity of the initial datum is preserved over long times,  times that...

On the regularity of abstract Cauchy problems and boundary value problems

Philippe Clément, Sylvie Guerre-Delabrière (1998)

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

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Maximal regularity (in L p -sense) for abstract Cauchy problems of order one and boundary value problems of order two is studied. In general, regularity of the first problems implies regularity of the second ones; the converse is shown to hold if the underlying Banach space has the UMD property. A stronger notion of regularity, introduced by Sobolevskii, plays an important role in the proofs.