On the Cauchy problem for a class of parabolic equations with variable density
Shoshana Kamin; Robert Kersner; Alberto Tesei
- Volume: 9, Issue: 4, page 279-298
- ISSN: 1120-6330
Access Full Article
topAbstract
topHow to cite
topReferences
top- Aronson, D. G., Uniqueness of positive weak solutions of second order parabolic equations. Ann. Polon. Math., 16, 1965, 285-303. Zbl0137.29403MR176231
- Aronson, D. G. - Crandall, M. - Peletier, L. A., Stabilization of solutions in a degenerate nonlinear diffusion problem. Nonlin. Anal., 6, 1982, 1001-1022. Zbl0518.35050MR678053DOI10.1016/0362-546X(82)90072-4
- Bertsch, M. - Kersner, R. - Peletier, L. A., Positivity versus localization in degenerate diffusion equations. Nonlin. Anal., 9, 1985, 987-1008. Zbl0596.35073MR804564DOI10.1016/0362-546X(85)90081-1
- Borok, V. M. - Zitomirskii, Ja. I., Cauchy problem for parabolic systems, degenerating at infinity. Zap. Mech. Mat. Fak. Chark. Gos. Univ. im Gorkogo i Cark. Mat. Obzhestva, 29, 1963, 5-15 (in Russian).
- Eidel'man, S. D., Parabolic systems. North-Holland, Amsterdam1969. Zbl0181.37403MR252806
- Eidus, D., The Cauchy problem for the nonlinear filtration equation in an inhomogeneous medium. J. Differ. Equations, 84, 1990, 309-318. Zbl0707.35074MR1047572DOI10.1016/0022-0396(90)90081-Y
- Eidus, D., The perturbed Laplace operator in a weighted . J. Funct. Anal., 100, 1991, 400-410. Zbl0762.35020MR1125232DOI10.1016/0022-1236(91)90117-N
- Eidus, D. - Kamin, S., The filtration equation in a class of functions decreasing at infinity. Proc. Amer. Math. Soc., 120, 1994, 825-830. Zbl0791.35065MR1169025DOI10.2307/2160476
- Feller, W., The parabolic differential equations and the associated semi-groups of transformations. Ann. Math., 55, 1952, 468-519. Zbl0047.09303MR47886
- Freidlin, M., Functional integration and partial differential equations. Princeton University Press, Princeton1985. Zbl0568.60057MR833742
- Friedman, A., On the uniqueness of the Cauchy problem for parabolic equations. Amer. J. Math., 81, 1959, 503-511. Zbl0086.30001MR104907
- Hasminsky, R. Z., Ergodic properties of recurrent diffusion processes and stabilization of the solution of the Cauchy problem for parabolic equations. Theory Prob. Appl., 5, 1970, 196-214 (in Russian). Zbl0106.12001MR133871
- Hille, E., Les probabilités continues en chaîne. C.R. Acad. Sci. Paris, 230, 1950, 34-35. Zbl0036.08801MR32119
- Holmgren, E., Sur les solutions quasianalytiques de l’équation de la chaleur. Ark. Mat., 18, 1924, 64-95. JFM50.0337.02
- Il'in, A. M. - Kalashnikov, A. S. - Oleinik, O. A., Linear equations of the second order of parabolic type. Russian Math. Surveys, 17, 1962, 1-144.
- Kamin, S. - Rosenau, P., Non-linear diffusion in a finite mass medium. Comm. Pure Appl. Math., 35, 1982, 113-127. Zbl0469.35060MR637497DOI10.1002/cpa.3160350106
- Kamynin, L. I. - Himtsenko, B., On Tikhonov-Petrowsky problem for second order parabolic equations. Sibirsky Math. J., 22, 1981, 78-109 (in Russian). Zbl0501.35040MR632819
- Lunardi, A., Schauder theorems for linear elliptic and parabolic problems with unbounded coefficients in . Studia Math., 128, 1998, 171-198. Zbl0899.35014MR1490820
- Murata, M., Non-uniqueness of the positive Cauchy problem for parabolic equations. J. Differ. Equations, 123, 1995, 343-387. Zbl0843.35036MR1362880DOI10.1006/jdeq.1995.1167
- Petrowsky, I. G., On some problems in the theory of partial differential equations. Usp. Mat. Nauk, 1, 1946, 44-70 (in Russian).
- Pinchover, Y., On uniqueness and nonuniqueness of the positive Cauchy problem for parabolic equations with unbounded coefficients. Math. Z., 223, 1996, 569-586. Zbl0869.35010MR1421956DOI10.1007/PL00004275
- Pinsky, R. G., Positive harmonic functions and diffusion. Cambridge University Press, Cambridge1995. Zbl0858.31001MR1326606DOI10.1017/CBO9780511526244
- Smirnova, G. N., The Cauchy problem for degenerate at infinity parabolic equations. Math. Sb., 70, 1966, 591-604 (in Russian). Zbl0152.30101MR199563
- Sonin, I. M., On the classes of uniqueness for degenerate parabolic equations. Math. Sb., 85, 1971, 459-473 (in Russian). Zbl0243.35050MR287167
- Täcklind, S., Sur les classes quasianalytiques de solutions des équations aux derivées partielles du type parabolique. Nord. Acta Reg. Soc. Sci. Uppsal., 10, 1936, 3-55. JFM62.1186.01
- Tikhonov, A. N., Théorèmes d’unicité pour l’équation de la chaleur. Math. Sb., 42, 1935, 199-216. Zbl0012.35501JFM61.1203.05
- Widder, D. V., Positive temperatures on an infinite rod. Trans. Amer. Math. Soc., 55, 1944, 85-95. Zbl0061.22303MR9795
- Zitomirski, Ja. I., Uniqueness classes for solutions of the Cauchy problem. Soviet. Math. Dokl., 8, 1967, 259-262. Zbl0153.41601