Artículo
Rial, D.F.; Rossi, J.D. "Localization of blow-up points for a parabolic system with a nonlinear boundary condition" (1999) Rendiconti del Circolo Matematico di Palermo. 48(1):135-152
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Abstract:
The authors localize the blow-up points of positive solutions of the system μ t = Δu, v t = Δv with conditions ∂u/∂η = f(v), ∂v/∂η = g(u) at the boundary of a bounded smooth domain Θ under some restrictions of f and g and the initial data (Δu 0, Δν 0 >c > 0). If Θ is a ball, the hypothesis on the initial data can be removed. © 1999 Springer.
Registro:
| Documento: | Artículo |
| Título: | Localization of blow-up points for a parabolic system with a nonlinear boundary condition |
| Autor: | Rial, D.F.; Rossi, J.D. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina |
| Palabras clave: | blow up; nonlinear boundary conditions; parabolic systems |
| Año: | 1999 |
| Volumen: | 48 |
| Número: | 1 |
| Página de inicio: | 135 |
| Página de fin: | 152 |
| DOI: | http://dx.doi.org/10.1007/BF02844385 |
| Título revista: | Rendiconti del Circolo Matematico di Palermo |
| Título revista abreviado: | Rend. Circ. Mat. Palermo |
| ISSN: | 0009725X |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0009725X_v48_n1_p135_Rial |
Referencias:
- Amann, H., Dynamic Theory of Quasilinear Parabolic Systems III. Global Existence (1989) Math. Z, 202 (2), pp. 219-254
- Deng, K., Global existence and nonexistence for a parabolic system with a nonlinear boundary condition (1995) Math. Meth. Appl. Sci, 18, pp. 307-315
- Hu, B., Hong-Ming, Y., The Profile Near Blow-up Time for the Solution of the Heat Equation with a Nonlinear Boundary Condition (1994) Trans. Amer. Math. Soc, 346 (1), pp. 117-135
- Ladyzenskaja, O., Solonnikov, V., Uralceva y, N., (1968) Linear and quasilinear equations of parabolic type
- Levine, H., Payne, L., Nonexistence theorems for the heat equation with non-linear boundary conditions and for the porous medium equation backward in time (1974) Jour. Differential Equations, 16 (2), pp. 319-334
- Lopez Gomez, J., Marquez, V., Wolanski, N., Blow-up Results and Localization of Blow-up Points for the Heat Equation with a Nonlinear Boundary Condition (1991) Jour. Diff. Eq., 92 (2), pp. 384-401
- Rial, D.F., Rossi, J.D., Blow-up Results and Localization of Blow-up Points in an N-Dimensional Smooth Domain (1997) Duke Math. Jour, 88 (2), pp. 391-405
- Rossi, J.D., Wolanski, N., Global Existence and Nonexistence for a Parabolic System with Nonlinear Boundary Conditions (1998) Diff. Int. Eq., 11, pp. 179-190
- Walter, W., On Existence and Nonexistence in the Large of Solutions of Parabolic Differential Equations with a Nonlinear Boundary Condition (1975) SIAM J. Math. Anal, 6 (1), pp. 85-90
Citas:
---------- APA ----------
Rial, D.F. & Rossi, J.D. (1999) . Localization of blow-up points for a parabolic system with a nonlinear boundary condition. Rendiconti del Circolo Matematico di Palermo, 48(1), 135-152.http://dx.doi.org/10.1007/BF02844385
---------- CHICAGO ----------
Rial, D.F., Rossi, J.D. "Localization of blow-up points for a parabolic system with a nonlinear boundary condition" . Rendiconti del Circolo Matematico di Palermo 48, no. 1 (1999) : 135-152.http://dx.doi.org/10.1007/BF02844385
---------- MLA ----------
Rial, D.F., Rossi, J.D. "Localization of blow-up points for a parabolic system with a nonlinear boundary condition" . Rendiconti del Circolo Matematico di Palermo, vol. 48, no. 1, 1999, pp. 135-152.http://dx.doi.org/10.1007/BF02844385
---------- VANCOUVER ----------
Rial, D.F., Rossi, J.D. Localization of blow-up points for a parabolic system with a nonlinear boundary condition. Rend. Circ. Mat. Palermo. 1999;48(1):135-152.http://dx.doi.org/10.1007/BF02844385
