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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.
@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},
     doi = {10.5802/afst.790},
     zbl = {0838.35064},
     mrnumber = {1344715},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.790/}
}
Stanislav Antontsev; Jesus Ildefonso Díaz; Serguei I. Shmarev. 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. doi : 10.5802/afst.790. https://afst.centre-mersenne.org/articles/10.5802/afst.790/

[1] Alt (H.W.) and Luckhaus (S.) .- Quasilinear elliptic-parabolic differential equations, Math. Z. 183 (1983), pp. 311-341. | MR 706391 | Zbl 0497.35049

[2] Antontsev (S.N.) .- 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 636152 | Zbl 0496.35051

[3] Antotsev (S.N.), Díaz (J.I.) and Shmarev (S.I.) .- 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] Antontsev (S.N.), Díaz (J.I.) and Shmarev (S.I.) .- 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 1229526

[5] Antontsev (S.N.) and Shmarev (S.I.) .- Localization of solutions of nonlinear parabolic equations with linear sources of general type, Dinamica Sploshnoi Sredy, Novosibirsk 89 (1989), pp. 28-42. | MR 1103219 | Zbl 0726.35020

[6] Antontsev (S.N.) and Shmarev (S.I.) .- 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 1127261 | Zbl 0772.35025

[7] Antontsev (S.N.) and Shmarev (S.I.) .- 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 1216393 | Zbl 0831.35083

[8] Bandle (C.) and Stakgold (I.) .- The formation of the dead core in parabolic reaction-diffusion problems, Trans. Amer. Math. Soc. 286 (1984), pp. 275-293. | MR 756040 | Zbl 0519.35042

[9] Bernis (F.) .- Existence results for double nonlinear higher order parabolic equations on unbounded domains, Math Annalen 279 (1988), pp. 373-394. | MR 922422 | Zbl 0609.35048

[10] Díaz (J.I.) and Hernández (J.) .- 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 741498 | Zbl 0533.35055

[11] Díaz (J.I.) and Hernández (J.) .- 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 901095 | Zbl 0643.35056

[12] Díaz (J.I.) and De Thélin (F.) .- On a nonlinear parabolic problem arising in some models related to turbulent flows, SIAM J. Math. 25, No 4 (1994), pp. 1085-1111. | MR 1278892 | Zbl 0808.35066

[13] Díaz (J.I.) and Veron (L.) .- Local vanishing properties of solutions of elliptic and parabolic quasilinear equations, Trans. Amer. Math. Soc. 290, No 2 (1985), pp. 787-814. | MR 792828 | Zbl 0579.35003

[14] Evans (L.C.) and Knerr (B.) .- Instantaneous shrinking of nonnegative solutions to certain nonlinear parabolic equations and variational inequalities, Illinois J. Math., 23 (1979), pp. 153-166. | MR 516577 | Zbl 0403.35052

[15] Galaktionov (V.A.) and Vazquez (J.L.) .- Extinction for a quasilinear heat equation with absorption II, A dynamical systems approach, to appear | MR 1284803 | Zbl 0831.35074

[16] Gilding (B.) and Kersner (R.) .- The characterization of reaction-convection-diffusion processes by travelling waves, Faculty of Applied Mathematics, University of Twente, Memorandum 1111 (1993).

[17] Kačur (J.) . - On a solution of degenerate elliptic-parabolic systems in Orlicz-Sobolev spacesII, Math. Z. 203 (1990), pp. 569-579. | MR 1044065 | Zbl 0659.35045

[18] Kalashnikov (A.S.) .- Some questions of the qualitative theory of nonlinear degenerate second-order parabolic equations, Russian Math Surveys 42, No 2 (1987), pp. 169-222. | MR 898624 | Zbl 0642.35047

[19] Kersner (R.) .- 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 516020 | Zbl 0396.35052

[20] Kersner (R.) .- Nonlinear heat conduction with absorption: space localization and extinction in finite time, SIAM J. Appl. Math. 43 (1983), pp. 1274-1285. | MR 722941 | Zbl 0536.35039

[21] Palimskii (I.) . - 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 876771 | Zbl 0579.35039

[22] Samarsky (A.A.), Galaktionov (V.A.), Kurdumov (S.P.) and Mikhaylov (A.M.) .- Blowup in Problems for Quasilinear Parabolic Problems, Nauka, Moscow (1987) (in Russian; English translation: Walter de Gruyter, Berlin, to appear).

[23] Shmarev (S.I.) .- Local properties of solutions of nonlinear equation of heat conduction with absorption, Dinamika Sploshnoi Sredy, Novosibirsk 95 (1990), pp. 28-42 (in Russian). | MR 1175705 | Zbl 0726.35020

[24] Shmarev (S.I.) . - The effect of support shrinking for solutions of a degenerate parabolic equation, Dinamica Sploshnoi Sredy 97 (1990), pp. 194-200 (in Russian). | MR 1175301 | Zbl 0745.35023