Abstract:
A system of heat equations with nonlinear coupling at the boundary is considered. Assuming that the solution is defined and bounded in a certain small time interval, conditions for the existence of solutions of the equations and the uniqueness of these solutions are proven.
Registro:
Documento: |
Artículo
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Título: | Uniqueness and non-uniqueness for a system of heat equations with nonlinear coupling at the boundary |
Autor: | Cortazar, C.; Elgueta, M.; Rossi, J.D. |
Ciudad: | Exeter |
Filiación: | Facultad de Matematicas, Universidad Catolica, Casilla 306 Correo 22, Santiago, Chile Departmento de Matemática, F.C.E y N., UBA (1428), Buenos Aires, Argentina
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Palabras clave: | Nonlinear equations; Theorem proving; Heat equations; Solution uniqueness; Partial differential equations |
Año: | 1999
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Volumen: | 37
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Número: | 2
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Página de inicio: | 257
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Página de fin: | 267
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DOI: |
http://dx.doi.org/10.1016/S0362-546X(98)00046-7 |
Título revista: | Nonlinear Analysis, Theory, Methods and Applications
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Título revista abreviado: | Nonlinear Anal Theory Methods Appl
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ISSN: | 0362546X
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CODEN: | NOAND
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v37_n2_p257_Cortazar |
Referencias:
- Aguirre, J., Escobedo, M., A Cauchy problem for ut -Δu = up: Asymptotic behavior of solutions (1986) Ann. Fac. Sci. Toulouse, 8, pp. 175-203
- Amann, H., Dynamic theory of quasi-linear parabolic systems III, global existence (1989) Math. Z., 202 (2), pp. 219-254
- Cortazar, C., Del Pino, M., Elgueta, M., On the short-time behaviour of the free boundary of a porous medium equation (1997) Duke J. Math., 87 (1), pp. 133-149
- Deng, K., Global existence and blow-up for a system of heat equations with non-linear boundary condition (1995) Math. Meth. Appl. Sci., 18, pp. 307-315
- Deng, K., Fila, M., Levine, H.A., On critical exponents for a system of heat equations coupled in the boundary conditions (1994) Acta Mat. Univ. Comenianae., 63, pp. 169-192
- Escobedo, M., Herreo, M.A., A uniqueness result for a semilinear reaction-diffusion system (1991) Proc. Am. Math. Soc., 112 (1), pp. 175-186
- Escobedo, M., Herrero, M.A., A semi-linear Parabolic System in a Bounded Domain (1993) Ann. Mat. Pura Appl., 165, pp. 315-336
- Friedman, A., (1994) Partial Differential Equations of Parabolic Type, , Prentice-Hall, Englewood Cliffs, NJ
- Fujita, H., Watanabe, S., On the uniqueness and non-uniqueness of solutions of initial value problems for some quasi-linear parabolic equations (1968) Commun. Pure Appl. Math., 21, pp. 631-652
- Hu, B., Yin, H.M., The profile near blowup time for solution of the heat equation with a nonlinear boundary condition (1994) Trans. Am. Math. Soc., 346 (1), pp. 117-135
- Hu, B., Yin, H.M., On critical exponents for the heat equation with a mixed nonlinear Dirichlet-Newmann nonlinear boundary condition (1997) J. Math. Anal. Appl., 209, pp. 683-711
- Rossi, J.D., Wolanski, N., Global Existence an Nonexistence for a Parabolic System with Nonlinear Boundary Conditions Diff. Int. Eq., , to appear
- Pao, C.V., (1992) Nonlinear Parabolic and Elliptic Equations, , Plenum Press, New York
Citas:
---------- APA ----------
Cortazar, C., Elgueta, M. & Rossi, J.D.
(1999)
. Uniqueness and non-uniqueness for a system of heat equations with nonlinear coupling at the boundary. Nonlinear Analysis, Theory, Methods and Applications, 37(2), 257-267.
http://dx.doi.org/10.1016/S0362-546X(98)00046-7---------- CHICAGO ----------
Cortazar, C., Elgueta, M., Rossi, J.D.
"Uniqueness and non-uniqueness for a system of heat equations with nonlinear coupling at the boundary"
. Nonlinear Analysis, Theory, Methods and Applications 37, no. 2
(1999) : 257-267.
http://dx.doi.org/10.1016/S0362-546X(98)00046-7---------- MLA ----------
Cortazar, C., Elgueta, M., Rossi, J.D.
"Uniqueness and non-uniqueness for a system of heat equations with nonlinear coupling at the boundary"
. Nonlinear Analysis, Theory, Methods and Applications, vol. 37, no. 2, 1999, pp. 257-267.
http://dx.doi.org/10.1016/S0362-546X(98)00046-7---------- VANCOUVER ----------
Cortazar, C., Elgueta, M., Rossi, J.D. Uniqueness and non-uniqueness for a system of heat equations with nonlinear coupling at the boundary. Nonlinear Anal Theory Methods Appl. 1999;37(2):257-267.
http://dx.doi.org/10.1016/S0362-546X(98)00046-7