@article{AFST_1995_6_4_1_5_0,
author = {Antontsev, Stanislav and Ildefonso D{\'\i}az, Jesus and Shmarev, Serguei I.},
title = {The support shrinking properties for solutions of quasilinear parabolic equations with strong absorption terms},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {5--30},
publisher = {Universit\'e Paul Sabatier},
address = {Toulouse},
volume = {Ser. 6, 4},
number = {1},
year = {1995},
mrnumber = {1344715},
zbl = {0838.35064},
language = {en},
url = {http://www.numdam.org/item/AFST_1995_6_4_1_5_0/}
}
TY - JOUR AU - Antontsev, Stanislav AU - Ildefonso Díaz, Jesus AU - Shmarev, Serguei I. TI - The support shrinking properties for solutions of quasilinear parabolic equations with strong absorption terms JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 1995 SP - 5 EP - 30 VL - 4 IS - 1 PB - Université Paul Sabatier PP - Toulouse UR - http://www.numdam.org/item/AFST_1995_6_4_1_5_0/ LA - en ID - AFST_1995_6_4_1_5_0 ER -
%0 Journal Article %A Antontsev, Stanislav %A Ildefonso Díaz, Jesus %A Shmarev, Serguei I. %T The support shrinking properties for solutions of quasilinear parabolic equations with strong absorption terms %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 1995 %P 5-30 %V 4 %N 1 %I Université Paul Sabatier %C Toulouse %U http://www.numdam.org/item/AFST_1995_6_4_1_5_0/ %G en %F AFST_1995_6_4_1_5_0
Antontsev, Stanislav; Ildefonso Díaz, Jesus; Shmarev, Serguei I. The support shrinking properties for solutions of quasilinear parabolic equations with strong absorption terms. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 4 (1995) no. 1, pp. 5-30. http://www.numdam.org/item/AFST_1995_6_4_1_5_0/
[1] ) and ) .- Quasilinear elliptic-parabolic differential equations, Math. Z. 183 (1983), pp. 311-341. | MR | Zbl
[2] ) .- On the localization of solutions of nonlinear degenerate elliptic and parabolic equations, Dokl. Akad. Nauk. SSSR, 260, No 6 (1981), pp. 1289-1293 (in Russian; English translation in Soviet Math. Dokl., 24, No 2 (1981), pp. 420-424). | MR | Zbl
[3] ), ) and ) .- New applications of energy methods to parabolic free boundary problems, Uspekhi Mat. Nauk, 46, issue 6 (282) (1991), pp. 181-182 (in Russian; English translation: in Russian Mathematical Surveys, 46, No 6 (1991), pp. 193-194).
[4] ), ) and ) .- New results of the character of localization of solutions for elliptic and parabolic equations, Birkhäuser-Verlag, International Series of Numerical Mathematics 106 (1992), pp. 59-66. | MR
[5] ) and ) .- Localization of solutions of nonlinear parabolic equations with linear sources of general type, Dinamica Sploshnoi Sredy, Novosibirsk 89 (1989), pp. 28-42. | MR | Zbl
[6] ) and ) .- Local energy method and vanishing of weak solutions of nonlinear parabolic equations, Dokl. Akad, Nauk SSSR, 318, No 4 (1991), pp. 777-781 (in Russian; English translation: in Soviet Math. Doklady 43 (1991)). | MR | Zbl
[7] ) and ) .- Local energy method and vanishing properties of weak solutions of quasilinear parabolic equations. In Free boundary problems involving solids, J. Chadam and H. Rasmussen eds., Pitman Res. Notes in Math. Ser., 281, Longman (1993), pp. 2-5. | MR | Zbl
[8] ) and ) .- The formation of the dead core in parabolic reaction-diffusion problems, Trans. Amer. Math. Soc. 286 (1984), pp. 275-293. | MR | Zbl
[9] ) .- Existence results for double nonlinear higher order parabolic equations on unbounded domains, Math Annalen 279 (1988), pp. 373-394. | MR | Zbl
[10] ) and ) .- Some results on the existence of free boundaries for parabolic reaction-diffusion systems, In Trends in theory and pratice of nonlinear differential equations, V. Lakshmikkantham ed., Marcel Dekker (1984), pp. 149-156. | MR | Zbl
[11] ) and ) .- Qualitative properties of free boundaries for some nonlinear degerenate parabolic equations. In Nonlinear parabolic equations: qualitative properties of solutions, L. Boccardo and A. Tesei eds., Pitman 149 (1987), pp. 85-93. | MR | Zbl
[12] ) and ) .- On a nonlinear parabolic problem arising in some models related to turbulent flows, SIAM J. Math. 25, No 4 (1994), pp. 1085-1111. | MR | Zbl
[13] ) and ) .- Local vanishing properties of solutions of elliptic and parabolic quasilinear equations, Trans. Amer. Math. Soc. 290, No 2 (1985), pp. 787-814. | MR | Zbl
[14] ) and ) .- Instantaneous shrinking of nonnegative solutions to certain nonlinear parabolic equations and variational inequalities, Illinois J. Math., 23 (1979), pp. 153-166. | MR | Zbl
[15] ) and ) .- Extinction for a quasilinear heat equation with absorption II, A dynamical systems approach, to appear | MR | Zbl
[16] ) and ) .- The characterization of reaction-convection-diffusion processes by travelling waves, Faculty of Applied Mathematics, University of Twente, Memorandum 1111 (1993).
[17] ) . - On a solution of degenerate elliptic-parabolic systems in Orlicz-Sobolev spacesII, Math. Z. 203 (1990), pp. 569-579. | MR | Zbl
[18] ) .- Some questions of the qualitative theory of nonlinear degenerate second-order parabolic equations, Russian Math Surveys 42, No 2 (1987), pp. 169-222. | MR | Zbl
[19] ) .- On the behavior of temperature fronts in nonlinear heat-conductive media with absorption, Vestnik MGU, Ser. 1, Mathematics and Mechanics, 5 (1978), pp. 44-51. | MR | Zbl
[20] ) .- Nonlinear heat conduction with absorption: space localization and extinction in finite time, SIAM J. Appl. Math. 43 (1983), pp. 1274-1285. | MR | Zbl
[21] ) . - Some qualitative properties of solutions of equations of nonlinear heat conductivity with absorption, Chislennye Metody Mekhaniki Sploshnoi Sredy, Novosibirsk 16, No 1 (1985), pp. 136-145 (in Russian). | MR | Zbl
[22] ), ), ) and ) .- Blowup in Problems for Quasilinear Parabolic Problems, Nauka, Moscow (1987) (in Russian; English translation: Walter de Gruyter, Berlin, to appear).
[23] ) .- Local properties of solutions of nonlinear equation of heat conduction with absorption, Dinamika Sploshnoi Sredy, Novosibirsk 95 (1990), pp. 28-42 (in Russian). | MR | Zbl
[24] ) . - The effect of support shrinking for solutions of a degenerate parabolic equation, Dinamica Sploshnoi Sredy 97 (1990), pp. 194-200 (in Russian). | MR | Zbl
