Semi-classical analysis for proof extinction-property in finite time of solutions for parabolic equations with homogeneous main part and degenerate absorption potential

K. Stiepanova


degenerate nonlinear parabolic equation; diffusion--absorption; extinction-property of solutions; semi-classical analysis


Bandle C., Stakgold I. The formation of the dead core in parabolic reactiondi diffusion problems // Trans. Amer. Math. Soc., 1984. V. 286, 1. P. 275-293.

Chen Xu-Yan, Matano H., Mimura M. Finite-point extinction and continuity of interfaces in a nonlinear diffusion equation with strong absorption // J. Reine Angew. Math., 1995. V. 459, 1. P. 1-36.

Friedman A., Herrero M.A. Extinction properties of semilinear heat equations with strong absorption // J. Math. Anal. Appl., 1987. V. 124, 2. - P. 530-546.

Knerr B.F. The behavior of the support of solutions of the equation of nonlinear heat conduction with absorption in one dimension // Trans. Amer. Math. Soc., 1979. - V. 249, 2. - P. 409-424.

Payne L.E., Improperly Posed Problems in Partial Differential Equations. -SIAM, Philadelphia, 1975. - 62 p.

Straughan B. Instability, Nonexistence and Weighted Energy Methods in Fluid Dynamics and Related Theories. - Pitman, London, 1982. - 169 p.

Diaz J., Veron L. Local vanishing properties of solutions of elliptic and parabolic quasilinear equations. // Trans. Amer. Math. Soc., 1985. - 290:2. -P. 787-814.

Antontsev S., Diaz J., Shmarev S.I. The Support Shrinking Properties for Solutions of Quasilinear Parabolic Equations with Strong Absorption Terms. // Annales de la Faculte des Sciences de Toulouse Math., 1995. - 6:4. - P. 5-30.

Cwickel M. Weak type estimates for singular value and the number of bound states of Schriodinger operator // Ann. Math., 1977. - 106. - P. 93-100.

Kondratiev V.A., Veron L. Asymptotic behaviour of solutions of some nonlinear parabolic or elliptic equations. // Asymptotic Analysis., 1997. - 14.- P. 117-156.

Belaud Y. Heler B., Veron L. Long-time vanishing properties of solutions of sublinear parabolic equations and semi-classical limit of Schrödinger operator // Ann. Inst. Henri Poincarre Anal. nonlinear, 2001. - V. 1, 18. - P. 43-68.

Heler B. Semi-classical analysis for the Schriodinger operator and applications. - Lecture Notes in Math. 1336, Springer-Verlag, 1988. - 107 p.

Belaud Y., Shishkov A. Long-time extinction of solutions of some semilinear parabolic equations // J. Differ. Equat., 2007. - 238. - P. 64-86.

Belaud Y. Asymptotic estimates for a variational problem involving a quasilinear operator in the semi-classical limit // Annals of global analysis and geometry, 2004. - 26. - P. 271 - 313.

Alt H.W., Luckhaus S. Quasilinear elliptic-parabolic differential equations // Math. Z., 1983. -V. 183, 3. - P. 311-341.

Bernis F. Existence results for doubly nonlinear higher order parabolic equations on unbounded domain // Math. Am., 1988. - V. 279, 3. - P. 373-394.

Stiepanova K.V. Extinction of solutions for parabolic equations with double nonlinearity and a degenerate absorption potential // Ukrainian Mathematical Journal, 2014. - V. 66, 1. - P. 89-107.

Rosenblyum G. V. Distribution of the discrete spectrum of singular differential operators // Doklady Akad. Nauk USSR, 1972. - 202. - P. 1012-1015.

Lieb E.H., Thirring W. Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relations to Sobolev Inequalities // In Studies in Math. Phys., essay in honour of V. Bargmann, Princeton Univ. Press, 1976. - P. 203-237.


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