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Abstract:

We study systems with different diffusions (local and nonlocal), mixed boundary conditions, and reaction terms. We prove existence and uniqueness of the solutions and then analyze global existence vs blow up in finite time. For blowing up solutions, we find asymptotic bounds for the blow-up rate. © 2018 Mauricio Bogoya and Julio D. Rossi.

Registro:

Documento: Artículo
Título:Systems with Local and Nonlocal Diffusions, Mixed Boundary Conditions, and Reaction Terms
Autor:Bogoya, M.; Rossi, J.D.
Filiación:Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia
Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon I 1428, Buenos Aires, Argentina
Año:2018
Volumen:2018
DOI: http://dx.doi.org/10.1155/2018/3906431
Título revista:Abstract and Applied Analysis
Título revista abreviado:Abstr. Appl. Anal.
ISSN:10853375
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10853375_v2018_n_p_Bogoya

Referencias:

  • Andreu-Vaillo, F., Mazen, J.M., Rossi, J., Toledo-Melero, J.J., (2010) Nonlocal Diffusion Problems of Mathematical Surveys and Monographs, 165. , American Mathematical Society, Real Sociedad Matematica EspaNola, Madrid, Providence, RI, USA
  • Bates, P.W., Fife, P.C., Ren, X., Wang, X., Travelingwavesin a convolution model for phase transitions (1997) Archive for Rational Mechanics and Analysis, 138 (2), pp. 105-136
  • Bogoya, M., A nonlocal nonlinear diffusion equation in higher space dimensions (2008) Journal of Mathematical Analysis and Appli-cations, 344 (2), pp. 601-615
  • Cortazar, C., Elgueta, M., Rossi, J.D., A nonlocal diffusion equation whose solutions develop a free boundary (2005) Annales Henri Poincare. A Journal of Theoretical and Mathematical Physics, 6 (2), pp. 269-281
  • Chasseigne, E., Chaves, M., Rossi, J.D., Asymptotic behavior for nonlocal diffusion equations (2006) Journal de Mathematiques Pureset Appliquees, 86 (3), pp. 271-291
  • Fife, P., Some nonclassical trends in parabolic and parabolic-like evolutions (2003) Trends in Nonlinear Analysis, pp. 153-191. , Springer, Berlin, Germany
  • Garcia-Melian, J., Rossi, J.D., On the principal eigenvalue of some nonlocal diffusion problems (2009) Journal of Differential Equations, 246 (1), pp. 21-38
  • Perez-Llanos, M., Rossi, J.D., Blow-up for a non-local diffusion problem with Neumann boundary conditions and a reaction term (2009) Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal, 70 (4), pp. 1629-1640
  • Bogoya, M., On non-local reaction-diffusion system in a bounded domain (2018) Boundary Value Problems, p. 16. , PaperNo. 38
  • Escobedo, M., Herrero, M.A., A semilinear parabolic system in a bounded domain (1993) Annali di Matematica Pura Ed Applicata. Serie Quarta, 165, pp. 315-336
  • Bandle, C., Brunner, H., Blow-up in diffusion equations (1998) Journal of Computational and Applied Mathematics, 97 (1-2), pp. 3-22

Citas:

---------- APA ----------
Bogoya, M. & Rossi, J.D. (2018) . Systems with Local and Nonlocal Diffusions, Mixed Boundary Conditions, and Reaction Terms. Abstract and Applied Analysis, 2018.
http://dx.doi.org/10.1155/2018/3906431
---------- CHICAGO ----------
Bogoya, M., Rossi, J.D. "Systems with Local and Nonlocal Diffusions, Mixed Boundary Conditions, and Reaction Terms" . Abstract and Applied Analysis 2018 (2018).
http://dx.doi.org/10.1155/2018/3906431
---------- MLA ----------
Bogoya, M., Rossi, J.D. "Systems with Local and Nonlocal Diffusions, Mixed Boundary Conditions, and Reaction Terms" . Abstract and Applied Analysis, vol. 2018, 2018.
http://dx.doi.org/10.1155/2018/3906431
---------- VANCOUVER ----------
Bogoya, M., Rossi, J.D. Systems with Local and Nonlocal Diffusions, Mixed Boundary Conditions, and Reaction Terms. Abstr. Appl. Anal. 2018;2018.
http://dx.doi.org/10.1155/2018/3906431