Abstract:
We deal with boundary value problems (prescribing Dirichlet or Neumann boundary conditions) for a nonlocal nonlinear diffusion operator which is analogous to the porous medium equation. First, we prove existence, uniqueness and the validity of a comparison principle for these problems. Next, we impose boundary data that blow up in finite time and study the behavior of the solutions. © 2007.
Registro:
Documento: |
Artículo
|
Título: | A nonlocal nonlinear diffusion equation with blowing up boundary conditions |
Autor: | Bogoya, M.; Ferreira, R.; Rossi, J.D. |
Filiación: | Departamento de Matemática, Universidad Católica de Chile, Santiago, Chile Departamento de Matemática, Universidad Nacional de Colombia, Bogotá, Colombia Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040, Spain Departamento Matematica, FCEyN, UBA, Buenos Aires, Argentina
|
Palabras clave: | Neumann boundary conditions; Nonlocal diffusion |
Año: | 2008
|
Volumen: | 337
|
Número: | 2
|
Página de inicio: | 1284
|
Página de fin: | 1294
|
DOI: |
http://dx.doi.org/10.1016/j.jmaa.2007.04.049 |
Título revista: | Journal of Mathematical Analysis and Applications
|
Título revista abreviado: | J. Math. Anal. Appl.
|
ISSN: | 0022247X
|
PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0022247X_v337_n2_p1284_Bogoya.pdf |
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v337_n2_p1284_Bogoya |
Referencias:
- Aronson, D.G., The porous medium equation (1986) Lecture Notes in Math., 1224. , Nonlinear Diffusion Problems. Fasano A., and Primicerio M. (Eds), Springer-Verlag
- Bates, P., Fife, P., Ren, X., Wang, X., Travelling waves in a convolution model for phase transitions (1997) Arch. Ration. Mech. Anal., 138, pp. 105-136
- Chen, X., Existence, uniqueness and asymptotic stability of travelling waves in nonlocal evolution equations (1997) Adv. Differential Equations, 2, pp. 125-160
- Cortazar, C., Elgueta, M., Localization and boundedness of the solutions of the Neumann problem for a filtration equation (1989) Nonlinear Anal., 13 (1), pp. 33-41
- Cortazar, C., Elgueta, M., Rossi, J.D., A non-local diffusion equation whose solutions develop a free boundary (2005) Ann. Henri Poincaré, 6 (2), pp. 269-281
- Cortazar, C., Elgueta, M., Vazquez, J.L., Diffusivity determination in nonlinear diffusion (1991) European J. Appl. Math., 2, pp. 159-169
- Fife, P., Some nonclassical trends in parabolic and parabolic-like evolutions (2003) Trends in Nonlinear Analysis, pp. 153-191. , Springer-Verlag, Berlin
- Galaktionov, V.A., Samarskii, A.A., Methods of constructing approximate self-similar solutions of nonlinear heat equations. I (1983) Mat. USSR Sb., 46, pp. 291-321
- Galaktionov, V.A., Vázquez, J.L., The problem of blow-up in nonlinear parabolic equations (2002) Discrete Contin. Dyn. Syst., 8 (2), pp. 399-433
- Gilding, B.H., Herrero, M.A., Localization and blow-up of thermal waves in nonlinear heat conduction with peaking (1988) Math. Ann., 282, pp. 223-242
- Samarskii, A.A., Galaktionov, V.A., Kurdyumov, S.P., Mikhailov, A.P., (1987) Blow-Up in Problems for Quasilinear Parabolic Equations, , Nauka, Moscow (in Russian); English transl.:
- Samarskii, A.A., Galaktionov, V.A., Kurdyumov, S.P., Mikhailov, A.P., (1995), Walter de Gruyter, Berlin; Vazquez, J.L., An introduction to the mathematical theory of the porous medium equation (1992) Shape Optimization and Free Boundaries, pp. 347-389. , Delfour M.C. (Ed), Dordrecht, Boston and Leiden
- Wang, X., Metaestability and stability of patterns in a convolution model for phase transitions (2002) J. Differential Equations, 183, pp. 434-461
Citas:
---------- APA ----------
Bogoya, M., Ferreira, R. & Rossi, J.D.
(2008)
. A nonlocal nonlinear diffusion equation with blowing up boundary conditions. Journal of Mathematical Analysis and Applications, 337(2), 1284-1294.
http://dx.doi.org/10.1016/j.jmaa.2007.04.049---------- CHICAGO ----------
Bogoya, M., Ferreira, R., Rossi, J.D.
"A nonlocal nonlinear diffusion equation with blowing up boundary conditions"
. Journal of Mathematical Analysis and Applications 337, no. 2
(2008) : 1284-1294.
http://dx.doi.org/10.1016/j.jmaa.2007.04.049---------- MLA ----------
Bogoya, M., Ferreira, R., Rossi, J.D.
"A nonlocal nonlinear diffusion equation with blowing up boundary conditions"
. Journal of Mathematical Analysis and Applications, vol. 337, no. 2, 2008, pp. 1284-1294.
http://dx.doi.org/10.1016/j.jmaa.2007.04.049---------- VANCOUVER ----------
Bogoya, M., Ferreira, R., Rossi, J.D. A nonlocal nonlinear diffusion equation with blowing up boundary conditions. J. Math. Anal. Appl. 2008;337(2):1284-1294.
http://dx.doi.org/10.1016/j.jmaa.2007.04.049