A fatou theorem for the equation u t = Δ(u - 1) +
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...
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2000
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| LEADER | 04033caa a22003857a 4500 | ||
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| 001 | PAPER-2183 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518203134.0 | ||
| 008 | 190411s2000 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-33646847952 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Korten, M.K. | |
| 245 | 1 | 2 | |a A fatou theorem for the equation u t = Δ(u - 1) + |
| 260 | |c 2000 | ||
| 270 | 1 | 0 | |m Departamento De MatemáTica, Fac. De Ciencias Exactas Y Naturales, Universidad De Buenos Aires, Pab. No. 1, Ciudad Universitaria, Argentina |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a 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 | ||
| 504 | |a 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 | ||
| 504 | |a 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] | ||
| 504 | |a 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 | ||
| 504 | |a 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 | ||
| 504 | |a 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 | ||
| 504 | |a 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 | ||
| 504 | |a 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 | ||
| 520 | 3 | |a 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. |l eng | |
| 593 | |a Departamento De MatemáTica, Fac. De Ciencias Exactas Y Naturales, Universidad De Buenos Aires, Pab. No. 1, Ciudad Universitaria, Argentina | ||
| 593 | |a Inst. Argentino De MatemáTica, Saavedra 15, Ser. Piso, Argentina | ||
| 593 | |a Department of Mathematics, University of Liousville, Louisville, Kentucky 40292, United States | ||
| 773 | 0 | |d 2000 |g v. 128 |h pp. 439-444 |k n. 2 |p Proc. Am. Math. Soc. |x 00029939 |w (AR-BaUEN)CENRE-347 |t Proceedings of the American Mathematical Society | |
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| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00029939_v128_n2_p439_Korten |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v128_n2_p439_Korten |y Registro en la Biblioteca Digital |
| 961 | |a paper_00029939_v128_n2_p439_Korten |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 63136 | ||