Artículos de revistas
A Singular Parabolic Equation With Logarithmic Nonlinearity And Lp-initial Data
Registro en:
Journal Of Differential Equations. , v. 249, n. 2, p. 349 - 365, 2010.
220396
10.1016/j.jde.2010.03.019
2-s2.0-77952646939
Autor
Ferreira L.C.F.
de Queiroz O.S.
Institución
Resumen
We study a parabolic equation with logarithmic nonlinearity and homogeneous Dirichlet condition in a smooth bounded domain. We firstly prove a result about existence of positive solutions with initial data in Lp-spaces, 1<p<∞; in order to overcome the singular logarithmic nonlinearity, among other arguments, we employ Hardy's inequality. After, the life span of the obtained solutions is studied. In particular we show a connection between global existence and solutions of the associated elliptic problem. © 2010 Elsevier Inc. 249 2 349 365 Bertozzi, A.L., Pugh, M.C., Finite-time blow-up of solutions of some long-wave unstable thin film equations (2000) Indiana Univ. Math. J., 49 (4), pp. 1323-1366 Brezis, H., Cazenave, T., A nonlinear heat equation with singular initial data (1996) J. Anal. Math., 68, pp. 277-304 Brezis, H., Cazenave, T., Martel, Y., Ramiandrisoa, A., Blow up for ut-Δu=g(u) revisited (1996) Adv. Differential Equations, 1 (1), pp. 73-90 Cazenave, T., Dickstein, F., Escobedo, M., A semilinear heat equation with concave-convex nonlinearity (1999) Rend. Mat. Appl. (7), 19 (2), pp. 211-242 Cazenave, T., Haraux, A., An introduction to semilinear evolution equations (1998) Oxford Lecture Ser. Math. Appl., 13. , Translated from the 1990 French original by Yvan Martel and revised by the authors, The Clarendon Press, Oxford University Press, New York Cazenave, T., Haraux, A., Équations d'évolution avec non linéarité logarithmique (1980) Ann. Fac. Sci. Toulouse Math., 2, pp. 21-51 Edmunds, D.E., Hurri-Syrjänen, R., Weighted Hardy inequalities (2005) J. Math. Anal. Appl., 310 (2), pp. 424-435 Galaktionov, V.A., Vázquez, J.L., The problem of blow-up in nonlinear parabolic equations (2002) Discrete Contin. Dyn. Syst., 8 (2), pp. 399-433. , Current Developments in Partial Differential Equations Giga, Y., Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system (1986) J. Differential Equations, 62 (2), pp. 186-212 Kato, T., Strong Lp solutions of the Navier-Stokes equations in the Rm with applications (1984) Math. Z., 187, pp. 471-480 Kato, T., Perturbation theory for linear operators (1966) Grundlehren Math. Wiss., 132. , Springer-Verlag, New York Montenegro, M., de Queiroz, O.S., Existence and regularity to an elliptic equation with logarithmic nonlinearity (2009) J. Differential Equations, 246 (2), pp. 482-511 Ni, W.-M., Sacks, P., Singular behavior in nonlinear parabolic equations (1985) Trans. Amer. Math. Soc., 287 (2), pp. 657-671 Salin, T., On quenching with logarithmic singularity (2003) Nonlinear Anal., 52, pp. 261-289 Weissler, F.B., Local existence and nonexistence for semilinear parabolic equations in Lp (1980) Indiana Univ. Math. J., 29 (1), pp. 79-102 Weissler, F.B., Semilinear evolution equations in Banach spaces (1979) J. Funct. Anal., 32 (3), pp. 277-296