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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
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
Palabras clave:Nonlinear equations; Theorem proving; Heat equations; Solution uniqueness; Partial differential equations
Año:1999
Volumen:37
Número:2
Página de inicio:257
Página de fin:267
DOI: http://dx.doi.org/10.1016/S0362-546X(98)00046-7
Título revista:Nonlinear Analysis, Theory, Methods and Applications
Título revista abreviado:Nonlinear Anal Theory Methods Appl
ISSN:0362546X
CODEN:NOAND
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