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

### Downloads

### References

2. 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.

3. 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.

4. 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.

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

6. 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.

8. 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.

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

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

11. 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.

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

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

14. 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.

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

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

17. 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.

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

19. 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.

*Visnyk of V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics*,

*84*, 31-45. Retrieved from https://periodicals.karazin.ua/mech_math/article/view/8568

The copyright holder is the **author**.

Authors who publish with this journal agree to the following terms:

1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's **authorship** and** initial publication in this journal.**

2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), **with an acknowledgement of its initial publication in this journal.**

3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).