Explosión y globalidad de soluciones para una ecuación de calor semilineal no autónoma con condición de Dirichlet

• Ceballos-Lira, Marcos Josías ^[1] ; Pérez, Aroldo ^[1]
  1. [1] Universidad Juárez Autónoma de Tabasco

     Universidad Juárez Autónoma de Tabasco

     México

     
• Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 53, Nº. 1, 2019, págs. 57-72
• Idioma: español
• DOI: 10.15446/recolma.v53n1.81042
• Títulos paralelos:
  • Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition
• Enlaces
  • Texto completo
• Resumen
  • español

    En este artículo demostramos la existencia local de una solución "mild" no negativa para una ecuación de calor semilineal no autónoma con condición de Dirichlet, y damos condiciones suficientes para la globalidad y la explosión en tiempo finito de la solución "mild". Nuestro enfoque para la existencia global se remonta a la técnica de Weissler y para la explosión en tiempo finito utilizamos la ultracontractividad intrínseca del semigrupo generado por el operador de difusión.

  • English

    In this paper we prove the local existence of a nonnegative mild solution for a nonautonomous semilinear heat equation with Dirichlet condition, and give sucient conditions for the globality and for the blow up infinite time of the mild solution. Our approach for the global existence goes back to the Weissler's technique and for the nite time blow up we uses the intrinsic ultracontractivity property of the semigroup generated by the diffusion operator.

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