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Abstract:

We provide examples of solutions to parabolic problems with non- trivial blow-up sets of dimension strictly smaller than the space dimension. To this end we just consider different diffusion operators in different variables, for example, ut = (um)xx + uyy + u m or ut = (|ux|p-2u x)x + uyy + up-1.For both equations, we prove that there exists a solution that blows up in the segment B(u) = [-L, L] ×{0}⊂ ℝ2. © 2007 American Mathematical Society.

Registro:

Documento: Artículo
Título:Nontrivial compact blow-up sets of smaller dimension
Autor:Perez-Llanos, M.; Rossi, J.D.
Filiación:Departamento de Matemáticas, Universidad Carlos III, Madrid, 28911 Leganés, Spain
Departamento de Matemáticas, Facultad de Clencias exactas y naturales, Universidad de Buenos Aires, Argentina
Palabras clave:Blow-up sets; P-laplacian; Porous media
Año:2008
Volumen:136
Número:2
Página de inicio:593
Página de fin:596
DOI: http://dx.doi.org/10.1090/S0002-9939-07-09028-4
Título revista:Proceedings of the American Mathematical Society
Título revista abreviado:Proc. Am. Math. Soc.
ISSN:00029939
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v136_n2_p593_PerezLlanos

Referencias:

  • Chen, X.Y., Matano, H., Convergence, asymptotic periodicity and finite point blow up in one-dimensional semilinear heat equations (1989) J. Differential Equations, 78, pp. 160-190. , MR986159 (90e:35018)
  • Cortázar, C., Del Pino, M., Elgueta, M., On the blow-up set for ut =Δum + u m, m> 1 (1998) Indiana Univ. Math. J., 47 (2), pp. 541-561. , MR1647932 (99h:35085)
  • Cortázar, C., Del Pino, M., Elgueta, M., Uniqueness and stability of regional blow-up in a porous-medium equation (2002) Ann. Inst. H. Poincare Anal. Non Lineaire., 19 (6), pp. 927-960. , MR193r9091 (2003h:35124)
  • Cortazar, C., Elgueta, M., Felmer, P., Symmetry in an elliptic problem and the blow-up set of a quasilinear heat equation (1996) Communications in Partial Differential Equations, 21 (3-4), pp. 507-520
  • Galaktionov, V.A., Vazquez, J.L., The problem of blow-up in nonlinear parabolic equations (2002) Discrete and Continuous Dynamical Systems, 8 (2), pp. 399-433
  • Merle, F., Solution of a nonlinear heat equation with arbitrarily given blow-up points (1992) Comm. Pure Appl. Math., 45, pp. 263-300. , MR1151268 (92k:35160)
  • Muller, C.E., Weissler, F.B., Single point blow up for a general semilinear heat equation (1983) Indiana Univ. Math. J., 34, pp. 881-913. , MR808833 (87a:35023)
  • Samarski, A., Galaktionov, V.A., Kurdyunov, S.P., Mikailov, A.P., Blow-up in quasilinear parabolic equations (1995) Walter de Gruyter, , Berlin, MR1330r922 (96b:35003)
  • Weissler, F.B., Single point blow up of semilinear initial boundary value problems (1984) J. Differential Equations, 55, pp. 204-224. , MR764124 (86a:35076)
  • Zaag, H., Determination of the curvature of the blow-up set and refined singular behavior for a semilinear heat equation Preprint, , MR2228461 (2007b:35189)
  • Zaag, H., On the regularity of the blow-up set for semilinear heat equations (2002) Ann. Inst. H. Poincaré Anal. Non Linéaire, 19 (5), pp. 505-542. , MR1922468 (2003h:35118)

Citas:

---------- APA ----------
Perez-Llanos, M. & Rossi, J.D. (2008) . Nontrivial compact blow-up sets of smaller dimension. Proceedings of the American Mathematical Society, 136(2), 593-596.
http://dx.doi.org/10.1090/S0002-9939-07-09028-4
---------- CHICAGO ----------
Perez-Llanos, M., Rossi, J.D. "Nontrivial compact blow-up sets of smaller dimension" . Proceedings of the American Mathematical Society 136, no. 2 (2008) : 593-596.
http://dx.doi.org/10.1090/S0002-9939-07-09028-4
---------- MLA ----------
Perez-Llanos, M., Rossi, J.D. "Nontrivial compact blow-up sets of smaller dimension" . Proceedings of the American Mathematical Society, vol. 136, no. 2, 2008, pp. 593-596.
http://dx.doi.org/10.1090/S0002-9939-07-09028-4
---------- VANCOUVER ----------
Perez-Llanos, M., Rossi, J.D. Nontrivial compact blow-up sets of smaller dimension. Proc. Am. Math. Soc. 2008;136(2):593-596.
http://dx.doi.org/10.1090/S0002-9939-07-09028-4