Singular perturbation in a nonlocal diffusion problem
We study a singular perturbation problem for a nonlocal evolution operator. The problem appears in the analysis of the propagation of flames in the high activation energy limit, when admitting nonlocal effects. We obtain uniform estimates and we show that, under suitable assumptions, limits are solu...
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| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
2006
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| LEADER | 06289caa a22006017a 4500 | ||
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| 003 | AR-BaUEN | ||
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| 008 | 190411s2006 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-31744437964 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Lederman, C. | |
| 245 | 1 | 0 | |a Singular perturbation in a nonlocal diffusion problem |
| 260 | |c 2006 | ||
| 270 | 1 | 0 | |m Lederman, C.; Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina; email: clederma@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
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| 504 | |a Berestycki, H., Caffarelli, L.A., Nirenberg, L., Uniform estimates for regularization of free boundary problems (1990) Analysis and Partial Differential Equations, 122, pp. 567-619. , Cora S., ed Lecture Notes in Pure and Applied Mathematics. New York: Marcel Dekker | ||
| 504 | |a Buckmaster, J.D., Ludford, G.S.S., (1982) Theory of Laminar Flames, , Cambridge: Cambridge University Press | ||
| 504 | |a Caffarelli, L.A., A Harnack inequality approach to the regularity of free boundaries. Part II: Flat free boundaries are Lipschitz (1989) Comm. Pure Appl. Math., 42, pp. 55-78 | ||
| 504 | |a Caffarelli, L.A., Uniform Lipschitz regularity of a singular perturbation problem (1995) Diff. Int. Eqs., 8 (7), pp. 1585-1590 | ||
| 504 | |a Caffarelli, L.A., Lederman, C., Wolanski, N., Uniform estimates and limits for a two phase parabolic singular perturbation problem (1997) Indiana Univ. Math. J., 46 (2), pp. 453-490 | ||
| 504 | |a Caffarelli, L.A., Lederman, C., Wolanski, N., Pointwise and viscosity solutions for the limit of a two phase parabolic singular perturbation problem (1997) Indiana Univ. Math. J., 46 (3), pp. 719-740 | ||
| 504 | |a Caffarelli, L.A., Vazquez, J.L., A free boundary problem for the heat equation arising in flame propagation (1995) Trans. Amer. Math. Soc., 347, pp. 411-441 | ||
| 504 | |a Coville, J., Travelling Wave in Non-local Reaction Diffusion Equation with Ignition Nonlinearity, , preprint | ||
| 504 | |a Fernández Bonder, J., Wolanski, N., A free boundary problem in combustion theory (2000) Interfaces Free Bound, 2, pp. 381-411 | ||
| 504 | |a Fife, P., Some nonclassical trends in parabolic and parabolic-like evolutions (2003) Trends in Nonlinear Analysis, pp. 153-191. , Berlin: Springer | ||
| 504 | |a Kamynin, L.I., Himcenko, B.N., On applications of the maximum principle to parabolic equations of second order (1972) Soviet Math. Doklady, 13 (3), pp. 683-686 | ||
| 504 | |a Ladyzenskaja, O., Solonnikov, V., Ural'ceva, N., (1988) Linear and Quasilinear Equations of Parabolic Type, 23. , Translations of Math. Mon. Amer. Math. Soc | ||
| 504 | |a Lederman, C., Wolanski, N., Viscosity solutions and regularity of the free boundary for the limit of an elliptic two phase singular perturbation problem (1998) Annali della Scuola Normale Sup. Pisa, Cl. Sci., Serie IV, 27 (2), pp. 253-288 | ||
| 504 | |a Lederman, C., Vázquez, J.L., Wolanski, N., Uniqueness of solution to a free boundary problem from combustion (2001) Transactions of the American Mathematical Society, 353 (2), pp. 655-692 | ||
| 504 | |a Souganidis, P., Recent developments in the theory of front propagation and its applications (2002) Modern Methods in Scientific Computing and Applications (Montreal, QC, 2001), 75, pp. 397-449. , NATO Sci. Ser. II Math. Phys. Chem., Dordrecht: Kluwer Acad. Publ | ||
| 504 | |a Vázquez, J.L., The free boundary problem for the heat equation with fixed gradient condition (1995) Proceedings International Conference on Free Boundary Problems and Applications, , Poland: Zakopane | ||
| 504 | |a Weiss, G.S., A singular limit arising in combustion theory: Fine properties of the free boundary (2003) Calculus of Variations and Partial Diff. Equations, 17 (3), pp. 311-340 | ||
| 504 | |a Zeldovich, Ya.B., Frank-Kamenetski, D.A., The theory of thermal propagation of flames (1938) Zh. Fiz. Khim., 12, pp. 100-105. , in Russian | ||
| 504 | |a (1992) Collected Works of Ya.B. Zeldovich, 1. , Princeton: Princeton Univ. Press | ||
| 520 | 3 | |a We study a singular perturbation problem for a nonlocal evolution operator. The problem appears in the analysis of the propagation of flames in the high activation energy limit, when admitting nonlocal effects. We obtain uniform estimates and we show that, under suitable assumptions, limits are solutions to a free boundary problem in a viscosity sense and in a pointwise sense at regular free boundary points. We study the nonlocal problem both for a single equation and for a system of two equations. Some of the results obtained are new even when the operator under consideration is the heat operator. |l eng | |
| 593 | |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina | ||
| 593 | |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina | ||
| 650 | 1 | 7 | |2 spines |a COMBUSTION |
| 690 | 1 | 0 | |a FREE BOUNDARY PROBLEM |
| 690 | 1 | 0 | |a NONLOCAL DIFFUSION |
| 690 | 1 | 0 | |a NONLOCAL EVOLUTION OPERATOR |
| 690 | 1 | 0 | |a VISCOSITY SOLUTIONS |
| 700 | 1 | |a Wolanski, N. | |
| 773 | 0 | |d 2006 |g v. 31 |h pp. 195-241 |k n. 2 |p Commun. Partial Differ. Equ. |x 03605302 |w (AR-BaUEN)CENRE-138 |t Communications in Partial Differential Equations | |
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| 856 | 4 | 0 | |u https://doi.org/10.1080/03605300500358111 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_03605302_v31_n2_p195_Lederman |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03605302_v31_n2_p195_Lederman |y Registro en la Biblioteca Digital |
| 961 | |a paper_03605302_v31_n2_p195_Lederman |b paper |c PE | ||
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