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De Pablo, A.; Quirós, F.; Rossi, J.D. "Nonsimultaneous quenching" (2002) Applied Mathematics Letters. 15(3):265-269
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Abstract:

We study the possibility of nonsimultaneous quenching for positive solutions of a coupled system of two semilinear heat equations, ut = uxx - v-p, vt = vxx - u-q, p, q > 0, with homogeneous Neumann boundary conditions and positive initial data. Under some assumptions on the initial data, we prove that if p,q ≥ 1, then quenching is always simultaneous, if p < 1 or q < 1, then there exists a wide class of initial data with nonsimultaneous quenching, and finally, if p < 1 ≤ q or q < 1 ≤ p, then quenching is always nonsimultaneous. We also give the quenching rates in all cases. © 2002 Elsevier Science Ltd. All rights reserved.

Registro:

Documento: Artículo
Título:Nonsimultaneous quenching
Autor:De Pablo, A.; Quirós, F.; Rossi, J.D.
Filiación:Departamento de Matemáticas, U. Carlos III de Madrid, 28911 Leganés, Spain
Departamento de Matemáticas, U. Autónoma de Madrid, 28049 Madrid, Spain
Departamento de Matemática, F.C.E y N., UBA, (1428) Buenos Aires, Argentina
Palabras clave:Quenching; Semilinear parabolic system
Año:2002
Volumen:15
Número:3
Página de inicio:265
Página de fin:269
DOI: http://dx.doi.org/10.1016/S0893-9659(01)00128-8
Título revista:Applied Mathematics Letters
Título revista abreviado:Appl Math Lett
ISSN:08939659
CODEN:AMLEE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08939659_v15_n3_p265_DePablo

Referencias:

  • Levine, H.A., The phenomenon of quenching: A survey (1985) Trends in the Theory and Practice of Nonlinear Analysis, pp. 275-286. , Edited by V. Lakshmikantham, Elsevier Science, North Holland
  • Kawarada, H., On solutions of initial-boundary problem ut = uxx + 1/(1 - U) (1975) Publ. Res. Inst. Math. Kyoto Univ., 10, pp. 729-736
  • Ke, L., Ning, S., Quenching for degenerate parabolic equations (1998) Nonlinear Anal., 34, pp. 1123-1135
  • Chan, C.Y., Recent advances in quenching phenomena (1996) Proc. Dynam. Systems. Appl., 2, pp. 107-113
  • Fila, M., Guo, J.S., Complete blow-up and incomplete quenching for the heat equation with nonlinear boundary conditions Nonlinear Anal., , to appear
  • Galaktionov, V., Vázquez, J.L., Necessary and sufficient conditions for complete blow-up and extintion for one dimensional quasilinear heat equations (1995) Arch. Rat. Mech. Anal., 129, pp. 225-244
  • Quirós, P., Rossi, J.D., Non-simultaneous blow-up in a semilinear parabolic system Z. Angew. Math. Phys., , to appear
  • Quirós, F., Rossi, J.D., Non-simultaneous Blow-up in a Nonlinear Parabolic System, , preprint

Citas:

---------- APA ----------
De Pablo, A., Quirós, F. & Rossi, J.D. (2002) . Nonsimultaneous quenching. Applied Mathematics Letters, 15(3), 265-269.
http://dx.doi.org/10.1016/S0893-9659(01)00128-8
---------- CHICAGO ----------
De Pablo, A., Quirós, F., Rossi, J.D. "Nonsimultaneous quenching" . Applied Mathematics Letters 15, no. 3 (2002) : 265-269.
http://dx.doi.org/10.1016/S0893-9659(01)00128-8
---------- MLA ----------
De Pablo, A., Quirós, F., Rossi, J.D. "Nonsimultaneous quenching" . Applied Mathematics Letters, vol. 15, no. 3, 2002, pp. 265-269.
http://dx.doi.org/10.1016/S0893-9659(01)00128-8
---------- VANCOUVER ----------
De Pablo, A., Quirós, F., Rossi, J.D. Nonsimultaneous quenching. Appl Math Lett. 2002;15(3):265-269.
http://dx.doi.org/10.1016/S0893-9659(01)00128-8