Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition

Marcos Josías Ceballos-Lira; Aroldo Pérez

doi:10.15446/recolma.v53n1.81042

Publicado

2019-01-01

Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition

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

DOI:

https://doi.org/10.15446/recolma.v53n1.81042

Palabras clave:

Reaction-diffusion equations, finite time blow up, Lévy processes, Dirichlet problem, ultracontractive semigroup, killed process (en)
Ecuaciones de reacción-difusión, explosión en tiempo finito, procesos de Lévy, problema de Dirichlet, semigrupo ultracontractivo, proceso matado (es)

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Autores/as

Marcos Josías Ceballos-Lira Universidad Juárez Autónoma de Tabasco - División Académica de Ciencias Básicas
Aroldo Pérez Universidad Juárez Autónoma de Tabasco - División Académica de Ciencias Básicas

Resumen (en)
Resumen (es)

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.

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.

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Cómo citar

APA

Ceballos-Lira, M. J. y Pérez, A. (2019). Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition. Revista Colombiana de Matemáticas, 53(1), 57–72. https://doi.org/10.15446/recolma.v53n1.81042

ACM

[1]

Ceballos-Lira, M.J. y Pérez, A. 2019. Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition. Revista Colombiana de Matemáticas. 53, 1 (ene. 2019), 57–72. DOI:https://doi.org/10.15446/recolma.v53n1.81042.

ACS

(1)

Ceballos-Lira, M. J.; Pérez, A. Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition. rev.colomb.mat 2019, 53, 57-72.

ABNT

CEBALLOS-LIRA, M. J.; PÉREZ, A. Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition. Revista Colombiana de Matemáticas, [S. l.], v. 53, n. 1, p. 57–72, 2019. DOI: 10.15446/recolma.v53n1.81042. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/81042. Acesso em: 10 jun. 2024.

Chicago

Ceballos-Lira, Marcos Josías, y Aroldo Pérez. 2019. «Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition». Revista Colombiana De Matemáticas 53 (1):57-72. https://doi.org/10.15446/recolma.v53n1.81042.

Harvard

Ceballos-Lira, M. J. y Pérez, A. (2019) «Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition», Revista Colombiana de Matemáticas, 53(1), pp. 57–72. doi: 10.15446/recolma.v53n1.81042.

IEEE

[1]

M. J. Ceballos-Lira y A. Pérez, «Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition», rev.colomb.mat, vol. 53, n.º 1, pp. 57–72, ene. 2019.

MLA

Ceballos-Lira, M. J., y A. Pérez. «Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition». Revista Colombiana de Matemáticas, vol. 53, n.º 1, enero de 2019, pp. 57-72, doi:10.15446/recolma.v53n1.81042.

Turabian

Ceballos-Lira, Marcos Josías, y Aroldo Pérez. «Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition». Revista Colombiana de Matemáticas 53, no. 1 (enero 1, 2019): 57–72. Accedido junio 10, 2024. https://revistas.unal.edu.co/index.php/recolma/article/view/81042.

Vancouver

1.

Ceballos-Lira MJ, Pérez A. Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition. rev.colomb.mat [Internet]. 1 de enero de 2019 [citado 10 de junio de 2024];53(1):57-72. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/81042

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CrossRef Cited-by

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1. Marcos J. Ceballos-Lira, Aroldo Pérez. (2020). Global Solutions and Blowing-Up Solutions for a Nonautonomous and Nonlocal in Space Reaction-Diffusion System with Dirichlet Boundary Conditions. Fractional Calculus and Applied Analysis, 23(4), p.1025. https://doi.org/10.1515/fca-2020-0054.