The support shrinking properties for solutions of quasilinear parabolic equations with strong absorption terms

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1. [1] Alt ( H.W.) and Luckhaus ( S.) .— Quasilinear elliptic-parabolic differential equations, Math. Z.183 (1983), pp. 311-341. Zbl0497.35049MR706391
2. [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). Zbl0496.35051MR636152
3. [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. [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 Mathematics106 (1992), pp. 59-66. MR1229526
5. [5] Antontsev ( S.N.) and Shmarev ( S.I.) .— Localization of solutions of nonlinear parabolic equations with linear sources of general type, Dinamica Sploshnoi Sredy, Novosibirsk89 (1989), pp. 28-42. Zbl0726.35020MR1103219
6. [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. Doklady43 (1991)). Zbl0772.35025MR1127261
7. [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. Zbl0831.35083MR1216393
8. [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. Zbl0519.35042MR756040
9. [9] Bernis ( F.) .— Existence results for double nonlinear higher order parabolic equations on unbounded domains, Math Annalen279 (1988), pp. 373-394. Zbl0609.35048MR922422
10. [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. Zbl0533.35055MR741498
11. [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., Pitman149 (1987), pp. 85-93. Zbl0643.35056MR901095
12. [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. Zbl0808.35066MR1278892
13. [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. Zbl0579.35003MR792828
14. [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. Zbl0403.35052MR516577
15. [15] Galaktionov ( V.A.) and Vazquez ( J.L.) .— Extinction for a quasilinear heat equation with absorption II, A dynamical systems approach, to appear Zbl0831.35074MR1284803
16. [16] Gilding ( B.) and Kersner ( R.) .— The characterization of reaction-convection-diffusion processes by travelling waves, Faculty of Applied Mathematics, University of Twente, Memorandum1111 (1993). 
17. [17] Kačur ( J.) . — On a solution of degenerate elliptic-parabolic systems in Orlicz-Sobolev spacesII, Math. Z.203 (1990), pp. 569-579. Zbl0659.35045MR1044065
18. [18] Kalashnikov ( A.S.) .— Some questions of the qualitative theory of nonlinear degenerate second-order parabolic equations, Russian Math Surveys42, No 2 (1987), pp. 169-222. Zbl0642.35047MR898624
19. [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. Zbl0396.35052MR516020
20. [20] Kersner ( R.) .- Nonlinear heat conduction with absorption: space localization and extinction in finite time, SIAM J. Appl. Math.43 (1983), pp. 1274-1285. Zbl0536.35039MR722941
21. [21] Palimskii ( I.) . — Some qualitative properties of solutions of equations of nonlinear heat conductivity with absorption, Chislennye Metody Mekhaniki Sploshnoi Sredy, Novosibirsk16, No 1 (1985), pp. 136-145 (in Russian). Zbl0579.35039MR876771
22. [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. [23] Shmarev ( S.I.) .— Local properties of solutions of nonlinear equation of heat conduction with absorption, Dinamika Sploshnoi Sredy, Novosibirsk95 (1990), pp. 28-42 (in Russian). Zbl0726.35020MR1175705
24. [24] Shmarev ( S.I.) . — The effect of support shrinking for solutions of a degenerate parabolic equation, Dinamica Sploshnoi Sredy97 (1990), pp. 194-200 (in Russian). Zbl0745.35023MR1175301