Dead cores and instantaneous compactification of the supports of energy solutions of quasilinear parabolic equations of arbitrary order

Sbornik Mathematics

Volumn 190, Issue 11-12, 1999, Pages 1843-1869

  Shishkov, A E ^a  

^a NONE

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EID: 0033478949     PISSN: 10645616     EISSN: 14684802     Source Type: Journal    
DOI: 10.1070/sm1999v190n12abeh000445     Document Type: Article

References (27)

1. A. S. Kalashnikov, "Some problems of the qualitative theory of nonlinear degenerate second-order parabolic equations", Uspekhi Mat. Nauk 42:2 (1987), 135-176; English transl. in Russian Math. Surveys 42:2.
2. A. S. Kalashnikov, "Some problems of the qualitative theory of nonlinear degenerate second-order parabolic equations", Uspekhi Mat. Nauk 42:2 (1987), 135-176; English transl. in Russian Math. Surveys 42:2.
3. S. N. Antontsev, J. I. Diaz, and S. I. Shmarev, "The support shrinking properties for solutions of quasilinear parabolic equations with strong absorption terms", Ann. Fac. Sci. Toulouse Math. (6) 4:1 (1995), 5-30.
4. F. Bernis, "Finite speed of propagations and asymptotic rates for some nonlinear higher order parabolic equations with absorption", Proc. Roy. Soc. Edinburgh Sect. A 104 (1986), 1-19.
5. L. C. Evans, and B. F. Knerr, "Instantaneous shrinking of the support of nonnegative solutions to certain nonlinear parabolic equations and variational inequalities", Illinois J. Math. 23:1 (1979), 153-166.
6. H. Brezis, and A. Friedman, "Estimates of the support of solutions of parabolic variational inequalities", Illinois J. Math. 20:1 (1976), 82-97.
7. A. S. Kalashnikov, "Instantaneous compactification of supports of solutions to semilinear parabolic equations and systems thereof", Mat. Zametki 47:1 (1990), 74-80; English transl. in Math. Notes 47 (1990).
8. A. S. Kalashnikov, "Instantaneous compactification of supports of solutions to semilinear parabolic equations and systems thereof", Mat. Zametki 47:1 (1990), 74-80; English transl. in Math. Notes 47 (1990).
9. R. Kersner and F. Nicolosi, "The nonlinear heat equations with absorption: effect of variable coefficients", J. Math. Anal. Appl. 170 (1992), 551-566.
10. A. S. Kalashnikov, "On the behavior of solutions of the Cauchy problem for parabolic systems with nonlinear dissipation near the initial hyperplane", Trudy Sem. Petrovsk. 16 (1992), 106-117; English transl. in J. Math. Sci. 69 (1992).
11. A. S. Kalashnikov, "On the behavior of solutions of the Cauchy problem for parabolic systems with nonlinear dissipation near the initial hyperplane", Trudy Sem. Petrovsk. 16 (1992), 106-117; English transl. in J. Math. Sci. 69 (1992).
12. M. Borelli and M. Ughi, "The fast diffusion equation with strong absorption: the instantaneous shrinking phenomenon", Rend. Instit. Mat. Univ. Trieste 26:1 2 (1994), 109-140.
13. U. G. Abdullaev, "Exact local estimates for the supports of solutions in problems for nonlinear parabolic equations", Mat. Sb. 186:8 (1995), 3-24; English transl. in Sb.: Math. 186 (1995).
14. U. G. Abdullaev, "Exact local estimates for the supports of solutions in problems for nonlinear parabolic equations", Mat. Sb. 186:8 (1995), 3-24; English transl. in Sb.: Math. 186 (1995).
15. A. S. Kalashnikov, "On quasilinear degenerating parabolic equations with singular lower-order terms and growing initial values", Differentsial'nye Uravneniya 29 (1993), 999-1009; English transl. in Differential Equations 29 (1993).
16. A. S. Kalashnikov, "On quasilinear degenerating parabolic equations with singular lower-order terms and growing initial values", Differentsial'nye Uravneniya 29 (1993), 999-1009; English transl. in Differential Equations 29 (1993).
17. R. Kersner and A. Shishkov, "Instantaneous shrinking of the support of energy solutions", J. Math. Anal. Appl. 198 (1996), 729-750.
18. S. N. Antontsev, "On the localization of solutions of nonlinear degenerate elliptic and parabolic equations", Dokl. Akad. Nauk SSSR 260 (1981), 1289-1293; English transl. in Soviet Math. Dokl. 24 (1981).
19. S. N. Antontsev, "On the localization of solutions of nonlinear degenerate elliptic and parabolic equations", Dokl. Akad. Nauk SSSR 260 (1981), 1289-1293; English transl. in Soviet Math. Dokl. 24 (1981).
20. C. Bandle and I. Stakgold, "The formation of a dead core in parabolic reaction-diffusion problems", Trans. Amer. Math. Soc. 286 (1984), 275-293.
21. J. I. Diaz and J. Hernandez, "Qualitative properties of free boundaries for some nonlinear degenerate parabolic equations", Nonlinear parabolic equations: qualitative properties of solutions. (Rome/Italy, 1985), Pitman Res. Notes Math. Ser. 149, Longman, Harlow 1987, pp. 85-93.
22. A. E. Shishkov, "Dead core and instantaneous shrinking of support of energy solutions of the quasilinear parabolic equations of arbitrary order", Preprint no. 97.03 of IAMM, NAS of Ukraine, June 1997.
23. N under optimal conditions on initial values", Indiana Univ. Math. J. 33 (1984), 51-87.
24. F. Bernis, "Existence results for doubly nonlinear higher order parabolic equations on unbounded domains", Math. Ann. 279 (1988), 373-394.
25. E. Di Benedetto and M. A. Herrero, "On the Cauchy problem and initial traces for a degenerate parabolic equation", Trans. Amer. Math. Soc. 314 (1989), 187-224.
26. A. E. Shishkov, "Evolution of the support of the solution with unbounded energy of a quasilinear degenerate parabolic equation of arbitrary order", Mat. Sb. 186:12 (1995), 151-172; English transl. in Sb.: Math. 186 (1995).
27. A. E. Shishkov, "Evolution of the support of the solution with unbounded energy of a quasilinear degenerate parabolic equation of arbitrary order", Mat. Sb. 186:12 (1995), 151-172; English transl. in Sb.: Math. 186 (1995).