Entropy solution for a nonlinear parabolic problem with homogeneous Neumann boundary condition involving variable exponents

• Autores: U. Traoré
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 23, Nº. 3, 2021, págs. 385-409
• Idioma: inglés
• DOI: 10.4067/S0719-06462021000300385
• Enlaces
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• Resumen
  • español

    RESUMEN En este artículo probamos la existencia y unicidad de una solución de entropía para una ecuación parabólica no lineal con condiciones de borde Neumann homogéneas y data inicial en L1. Usando una técnica de discretización del tiempo, analizamos las preguntas de existencia, unicidad y estabilidad. El contexto funcional involucra espacios de Lebesgue y Sobolev con exponentes variables.

  • English

    ABSTRACT In this paper we prove the existence and uniqueness of an entropy solution for a non-linear parabolic equation with homogeneous Neumann boundary condition and initial data in L1. By a time discretization technique we analyze the existence, uniqueness and stability questions. The functional setting involves Lebesgue and Sobolev spaces with variable exponents.

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