New approach to prove the existence of classical solutions for a class of nonlinear parabolic equations

• Autores: Svetlin Georgiev Georgiev, Khaled Zennir
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 20, Nº. 2, 2018, págs. 23-39
• Idioma: inglés
• DOI: 10.4067/S0719-06462018000200023
• Enlaces
  • Texto completo
• Resumen
  • español

    RESUMEN En este artículo, consideramos una clase de ecuaciones parabólicas nolineales. Usamos una representación integral combinada con una especie de teorema de punto fijo para probar la existencia de soluciones clásicas para el problema de valor inicial (1.1), (1.2). También obtenemos un resultado sobre la dependencia continua de la data inicial. Proponemos una estrategia nueva para la investigación de la existencia de soluciones clásicas de algunas clases de ecuaciones parabólicas nolineales.

  • English

    ABSTRACT In this article, we consider a class of nonlinear parabolic equations. We use an integral representation combined with a sort of fixed point theorem to prove the existence of classical solutions for the initial value problem (1.1), (1.2). We also obtain a result on continuous dependence on the initial data. We propose a new approach for investigation for existence of classical solutions of some classes nonlinear parabolic equations.

• Referencias bibliográficas
  • Braik, A.,Beniani, A.,Zennir, Kh.. (2017). Polynomial stability for system of 3 wave equations with infinite memories. Math. Meth. Appl. Sci.....
  • Braik, A.,Miloudi, Y.,Zennir, Kh.. (2017). A finite-time blow-up result for a class of solutions with positive initial energy for coupled...
  • Deng, K.. (1992). Comparison principle for some nonlocal problems. Quart. Appl. Math.. 50. 517
  • Fang, Z. B.,Zhang, J.. (2014). Global and blow-up solutions for the nonlocal p-Laplacian evolution equation with weighted nonlinear nonlocal...
  • Gao, Y.,Gao, W.. (2011). Existence and blow-up of solutions for a porous medium equation with nonlocal boundary condition. Appl. Anal.. 90....
  • Gladkov, A.,Guedda, M.. (2011). Blow-up problem for semilinear heat equation with absorption and a nonlocal boundary condition. Nonlinear...
  • Gladkov, A.,Guedda, M.. (2012). Semilinear heat equation with absorption and a nonlocal boundary condition. Appl. Anal.. 91. 2267
  • Gladkov, A.,Kim, K. I.. (2008). Blow-up of solutions for semilinear heat equation with nonlinear nonlocal boundary condition. J. Math. Anal....
  • Gladkov, A.,Kim, K. I.. (2009). Uniqueness and nonuniqueness for reaction-diffusion equation with nonlocal boundary condition. Adv. Math....
  • Gladkov, A.,Nikitin, A.. (2014). A reaction-diffusion system with nonlinear nonlocal boundary conditions. Int. J. Partial Differential Equations....
  • Liu, D.. (2016). Blow-up for a degenerate and singular parabolic equation with nonlocal boundary condition. J. Nonlinear Sci. Appl. 9. 208
  • Liu, D.,Mu, C.. (2010). Blowup properties for a semilinear reaction-diffusion system with nonlinear nonlocal boundary conditions. Abstr. Appl....
  • Samarskii, A.,Galaktionov, V.,Kurdyumov, S.,Mikhailov, A.. (1995). Blow-up in Quasilinear Parabolic Equations. Walter de Gruyer. Berlin.
  • Xiang, T.,Yuan, R.. (2009). A class of expansive type Krasnoselskii fixed point theorem.. Nonlinear Analysis. 3229
  • Zhong, G.,Tian, L.. (2012). Blow up problems for a degenerate parabolic equation with nonlocal source and nonlocal nonlinear boundary condition....
  • Zhou, J.,Yang, D.. (2015). Blowup for a degenerate and singular parabolic equation with nonlocal source and nonlocal boundary. Appl. Math....