Artículo
Korten, M.K. "A fatou theorem for the equation u t = Δ(u - 1) +" (2000) Proceedings of the American Mathematical Society. 128(2):439-444
Consulte la política de Acceso Abierto del editor
Abstract:
In one space dimension and for a given function u r(x) ∈ C 0 ∞ (say such that u 1(x) > 1 in some interval), the equation u t = Δ(u - 1) + can be thought of as describing the energy per unit volume in a Stefan-type problem where the latent heat of the phase change is given by 1 -u 1(x). Given a solution 0 ≤ u ∈ L loc 1(ℝ d× (0,T)) to this equation, we prove that for a.e. x 0 ∈ ℝ d, there exists lin (X,t)∈Γβk(x0), (X,t)→.x0 (u(x,t) -1) + = (f(x o) - 1) +, where f = ∂ μ/∂| | is the Radon-Nikodym derivative of the initial trace μ with respect to Lebesgue measure and Γ β k(x 0) = {|x -x 0| <√t, 0 < t < k} are the parabolic "non-tangential" approach regions. Since only (u - 1) + is continuous, while u is usually not, lim (X,t)∈Γβk(x0), (X,t)→.x0 u(x,t) = f(x 0) does not hold in general. ©1999 American Mathematical Society.
Registro:
| Documento: | Artículo |
| Título: | A fatou theorem for the equation u t = Δ(u - 1) + |
| Autor: | Korten, M.K. |
| Filiación: | Departamento De MatemáTica, Fac. De Ciencias Exactas Y Naturales, Universidad De Buenos Aires, Pab. No. 1, Ciudad Universitaria, Argentina Inst. Argentino De MatemáTica, Saavedra 15, Ser. Piso, Argentina Department of Mathematics, University of Liousville, Louisville, Kentucky 40292, United States |
| Año: | 2000 |
| Volumen: | 128 |
| Número: | 2 |
| Página de inicio: | 439 |
| Página de fin: | 444 |
| 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_v128_n2_p439_Korten |
Referencias:
- Andreucci, D., Korten, M.K., Initial traces of solutions to a one-phase Stefan problem in an infinite strip (1993) Rev. Mat. Iberoamericana, 9 (2), pp. 315-332. , [AK] MR 94m:35319
- Bouillet, J.E., Signed solutions to diffusion-heat conduction equations (1990) Pitman Res. Notes Math. Ser., 186, pp. 480-485. , [B] Free Boundary Problems: Theory and Applications, Proc. Int. Colloq. Irsce/Ger. 1987, Vol. II
- Bouillet, J.E., Korten, M.K., Márquez, V., Singular limits and the Mesa problem (1998) Rev. Union Mat. Argentina, 41 (1), pp. 27-40. , [BKM]
- Calderón, A.P., On the behaviour of harmonic functions at the boundary (1950) Trans. Amer. Math. Soc., 68, pp. 47-54. , [C] MR 11:357e
- Dahlberg, B.E.J., Fabes, E., Kenig, C.E., A Fatou theorem for solutions of the porous medium equation (1984) Proc. Amer. Math. Soc., 91, pp. 205-212. , [DFK] MR 85e:35064
- Dibenedetto, E., Continuity of weak solutions to certain singular parabolic equations (1982) Ann. Mat. Pura Appl. (4), 130, pp. 131-176. , [DB] MR 83k:35045
- Hui, K.M., Fatou theorem for the solutions of some nonlinear equations, 31 (1994) Math. Anal. Applic., 183, pp. 37-52. , [H] MR 95c:35125
- Krten, M.K., Non-negative solutions of u t = Δ(u -1) +: Regularity and uniqueness for the Cauchy problem (1996) Nonl. Anal., Th., Meth. and Appl, 27 (5), pp. 589-603. , [K] MR 97h:35089
Citas:
---------- APA ----------
(2000) . A fatou theorem for the equation u t = Δ(u - 1) +. Proceedings of the American Mathematical Society, 128(2), 439-444.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v128_n2_p439_Korten [ ]
---------- CHICAGO ----------
Korten, M.K. "A fatou theorem for the equation u t = Δ(u - 1) +" . Proceedings of the American Mathematical Society 128, no. 2 (2000) : 439-444.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v128_n2_p439_Korten [ ]
---------- MLA ----------
Korten, M.K. "A fatou theorem for the equation u t = Δ(u - 1) +" . Proceedings of the American Mathematical Society, vol. 128, no. 2, 2000, pp. 439-444.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v128_n2_p439_Korten [ ]
---------- VANCOUVER ----------
Korten, M.K. A fatou theorem for the equation u t = Δ(u - 1) +. Proc. Am. Math. Soc. 2000;128(2):439-444.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v128_n2_p439_Korten [ ]
