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Renormalized solutions of nonlinear parabolic equations with diffuse measure data

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Abstract

Given a parabolic cylinder Ω × (0, T), where Ω is a bounded domain of \({\mathbb{R}^N}\) , we consider IBV problems involving equations of the type

$$b(u)_{t} - \Delta_{p} u = \mu$$

where b is a increasing C 1-function and μ is a diffuse measure. We prove the existence and uniqueness of a renormalized solution for this class of nonlinear parabolic equations.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Raphaël Salem UMR 6085, CNRS-Université de Rouen, Avenue de l’Université, BP. 12 Technopôle du Madrillet, 76801, Saint-Étienne-du-Rouvray, France

    Dominique Blanchard

  2. Laboratoire d’anlyse numérique, Université Pierre et Marie-Curie, Case 187, 75252, Paris Cedex 05, France

    Dominique Blanchard

  3. Dipartimento di Scienze di Base e Applicate per l’ Ingegneria, “Sapienza”, Università di Roma, via Scarpa 16, Rome, 00161, Italy

    Francesco Petitta

  4. Faculté des Sciences Juridiques, Économiques et Sociales, Université Hassan 1, B.P. 784, Settat, Morocco

    Hicham Redwane

Authors
  1. Dominique Blanchard
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  2. Francesco Petitta
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  3. Hicham Redwane
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Correspondence to Francesco Petitta.

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Blanchard, D., Petitta, F. & Redwane, H. Renormalized solutions of nonlinear parabolic equations with diffuse measure data. manuscripta math. 141, 601–635 (2013). https://doi.org/10.1007/s00229-012-0585-7

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  • DOI: https://doi.org/10.1007/s00229-012-0585-7

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