RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Algebra i Analiz: Year: Volume: Issue: Page: Find

 Algebra i Analiz, 2007, Volume 19, Issue 2, Pages 105–121 (Mi aa115)

Research Papers

Admissible conditions for parabolic equations degenerating at infinity

Sh. Kamina, M. A. Poziob, A. Teseib

a School of Mathematical Sciences, Tel Aviv University, Tel-Aviv, Israel
b Dipartimento di Matematica "G. Castelnuovo", Università di Roma "La Sapienza", Roma, Italia

Abstract: Well-posedness in $L^\infty(\mathbb{R}^n)$ $(n\ge3)$ of the Cauchy problem is studied for a class of linear parabolic equations with variable density. In view of degeneracy at infinity, some conditions at infinity are possibly needed to make the problem well-posed. Existence and uniqueness results are proved for bounded solutions that satisfy either Dirichlet or Neumann conditions at infinity.

Keywords: Parabolic Cauchy problem, linear parabolic equations with variable density, bounded solutions.

Full text: PDF file (176 kB)
References: PDF file   HTML file

English version:
St. Petersburg Mathematical Journal, 2008, 19:2, 239–251

Bibliographic databases:

MSC: 35K15, 35K65
Language:

Citation: Sh. Kamin, M. A. Pozio, A. Tesei, “Admissible conditions for parabolic equations degenerating at infinity”, Algebra i Analiz, 19:2 (2007), 105–121; St. Petersburg Math. J., 19:2 (2008), 239–251

Citation in format AMSBIB
\Bibitem{KamPozTes07} \by Sh.~Kamin, M.~A.~Pozio, A.~Tesei \paper Admissible conditions for parabolic equations degenerating at infinity \jour Algebra i Analiz \yr 2007 \vol 19 \issue 2 \pages 105--121 \mathnet{http://mi.mathnet.ru/aa115} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2333899} \zmath{https://zbmath.org/?q=an:1152.35413} \elib{http://elibrary.ru/item.asp?id=9487750} \transl \jour St. Petersburg Math. J. \yr 2008 \vol 19 \issue 2 \pages 239--251 \crossref{https://doi.org/10.1090/S1061-0022-08-00996-5} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000267653200006} 

• http://mi.mathnet.ru/eng/aa115
• http://mi.mathnet.ru/eng/aa/v19/i2/p105

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Reyes G., Vázquez J.L., “The inhomogeneous PME in several space dimensions. Existence and uniqueness of finite energy solutions”, Commun. Pure Appl. Anal., 7:6 (2008), 1275–1294
2. Reyes G., Vázquez J.L., “Long time behavior for the inhomogeneous PME in a medium with slowly decaying density”, Commun. Pure Appl. Anal., 8:2 (2009), 493–508
3. Punzo F., Tesei A., “Uniqueness of solutions to degenerate elliptic problems with unbounded coefficients”, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 26:5 (2009), 2001–2024
4. Punzo F., “On the Cauchy problem for nonlinear parabolic equations with variable density”, J. Evol. Equ., 9:3 (2009), 429–447
5. Punzo F., “Uniqueness and non-uniqueness of bounded solutions to singular nonlinear parabolic equations”, Nonlinear Anal., 70:8 (2009), 3020–3029
6. Kamin S., Reyes G., Vázquez J.L., “Long time behavior for the inhomogeneous PME in a medium with rapidly decaying density”, Discrete and Continuous Dynamical Systems, 26:2 (2010), 521–549
7. Punzo F., “Phragmèn-Lindelöf principles for fully nonlinear elliptic equations with unbounded coefficients”, Commun. Pure Appl. Anal., 9:5 (2010), 1439–1461
8. Punzo F., “Well-posedness of the Cauchy problem for nonlinear parabolic equations with variable density in the hyperbolic space”, NoDEA Nonlinear Differential Equations Appl., 19:4 (2012), 485–501
9. Punzo F., “Uniqueness and support properties of solutions to singular quasilinear parabolic equations on surfaces of revolution”, Ann. Mat. Pura Appl., 191:2 (2012), 311–338
10. Punzo F., “Uniqueness and non-uniqueness of solutions to quasilinear parabolic equations with a singular coefficient on weighted Riemannian manifolds”, Asymptotic Anal., 79:3-4 (2012), 273–301
11. Nieto S., Reyes G., “Asymptotic Behavior of the Solutions of the Inhomogeneous Porous Medium Equation with Critical Vanishing Density”, Commun. Pure Appl. Anal, 12:2 (2013), 1123–1139
12. de Pablo A., Reyes G., Sánchez A., “The Cauchy problem for a nonhomogeneous heat equation with reaction”, Discrete Contin. Dyn. Syst., 33:2 (2013), 643–662
13. Li X., Xiang Zh., “Existence and Nonexistence of Local/Global Solutions For a Nonhomogeneous Heat Equation”, Commun. Pure Appl. Anal, 13:4 (2014), 1465–1480
14. Grillo G., Muratori M., Punzo F., “Conditions At Infinity For the Inhomogeneous Filtration Equation”, Ann. Inst. Henri Poincare-Anal. Non Lineaire, 31:2 (2014), 413–428
15. Kamin Sh., Punzo F., “Prescribed Conditions At Infinity For Parabolic Equations”, Commun. Contemp. Math., 17:1 (2015), 1450004
16. Punzo F., Valdinoci E., “Uniqueness in Weighted Lebesgue Spaces For a Class of Fractional Parabolic and Elliptic Equations”, J. Differ. Equ., 258:2 (2015), 555–587
17. Kamin Sh., Punzo F., “Dirichlet conditions at infinity for parabolic and elliptic equations”, Nonlinear Anal.-Theory Methods Appl., 138 (2016), 156–175
18. Punzo F., Strani M., “Dirichlet Boundary Conditions For Degenerate and Singular Nonlinear Parabolic Equations”, Potential Anal., 47:2 (2017), 151–168
19. Mastrolia P., Monticelli D.D., Punzo F., “Elliptic and Parabolic Equations With Dirichlet Conditions At Infinity on Riemannian Manifolds”, Adv. Differ. Equat., 23:1-2 (2018), 89–108
20. Punzo F., Valdinoci E., “Prescribed Conditions At Infinity For Fractional Parabolic and Elliptic Equations With Unbounded Coefficients”, ESAIM-Control OPtim. Calc. Var., 24:1 (2018), 105–127
21. A. B. Muravnik, “On qualitative properties of solutions to quasilinear parabolic equations admitting degenerations at infinity”, Ufa Math. J., 10:4 (2018), 77–84
•  Number of views: This page: 292 Full text: 84 References: 32 First page: 5