The Dirichlet problem associated to the relativistic heat equation

Andreu, F.; Caselles, Vicent; Mazón, José M.; Moll, Salvador

doi:10.1007/s00208-009-0428-3

Cited by 33 publications

(54 citation statements)

References 24 publications

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“…studied in [4,8,20,18] under different types of boundary conditions (compare condition (5.28) with (3.26) in [4], (34) in [8], (50) in [20], and condition 3 of Definition 8.3 in [18]). Therefore, the unique solutions of those problems belong as well to DT BV + (Ω).…”

Section: Homogeneous Neumann Boundary Conditions and More General Nonmentioning

confidence: 99%

Nonlinear diffusion in transparent media: The resolvent equation

Giacomelli

Moll

Petitta

2017

Advances in Calculus of Variations

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We consider the partial differential equationwith f nonnegative and bounded and m ∈ R. We prove existence and uniqueness of solutions for both the Dirichlet problem (with bounded and nonnegative boundary datum) and the homogeneous Neumann problem. Solutions, which a priori belong to a space of truncated bounded variation functions, are shown to have zero jump part with respect to the H N −1 Hausdorff measure. Results and proofs extend to more general nonlinearities.

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Section: Homogeneous Neumann Boundary Conditions and More General Nonmentioning

confidence: 99%

Nonlinear diffusion in transparent media: The resolvent equation

Giacomelli

Moll

Petitta

2017

Advances in Calculus of Variations

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“…The correct notion of weak trace is much more technical and is described in [10]. Using Lemma 5.7 in [8], one can directly obtain that v satisfies (2.4) in this generalized sense. Since we do not need this result here, we skip the details that would need several technical definitions to be fully explained.…”

Section: An Asymptotic Expansion Showsmentioning

confidence: 99%

On the relativistic heat equation in one space dimension

Carrillo

Caselles

Moll

2013

Proceedings of the London Mathematical Society

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“…On the other hand, the analysis similar to ours is in [13] and [14]. There is a description of D(J ) for the multidimensional version of the problem we consider, see for example, [6]. It is based on Anzellotti's formula for integration by parts [8].…”

Section: Cannot Belong To D(∂j )mentioning

confidence: 99%

Almost classical solutions to the total variation flow

2012

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Abstract. The paper examines the one-dimensional total variation flow equation with Dirichlet boundary conditions. Thanks to a new concept of "almost classical" solutions we are able to determine evolution of facets -flat regions of solutions. A key element of our approach is the natural regularity determined by the nonlinear elliptic operator, for which x 2 is an example of an irregular function. Such a point of view allows us to construct solutions. We apply this idea to numerical simulations for typical initial data. Due to the nature of Dirichlet data, any monotone function is an equilibrium. We prove that each solution reaches such a steady state in finite time.

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The Dirichlet problem associated to the relativistic heat equation

Abstract: We prove existence and uniqueness of entropy solutions for the nonhomogeneous Dirichlet problem associated to the relativistic heat equation. Mathematics Subject Classification

Cited by 33 publications

References 24 publications

Nonlinear diffusion in transparent media: The resolvent equation

Nonlinear diffusion in transparent media: The resolvent equation

On the relativistic heat equation in one space dimension

Almost classical solutions to the total variation flow

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