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

This article is cited in 21 scientific papers (total in 21 papers)

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.

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

Bibliographic databases:

MSC: 35K15, 35K65
Received: 01.12.2005

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
\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
\jour St. Petersburg Math. J.
\yr 2008
\vol 19
\issue 2
\pages 239--251

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    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  crossref  mathscinet  isi
    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  crossref  mathscinet  zmath  isi  elib
    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  crossref  mathscinet  zmath  adsnasa  isi
    4. Punzo F., “On the Cauchy problem for nonlinear parabolic equations with variable density”, J. Evol. Equ., 9:3 (2009), 429–447  crossref  mathscinet  zmath  isi
    5. Punzo F., “Uniqueness and non-uniqueness of bounded solutions to singular nonlinear parabolic equations”, Nonlinear Anal., 70:8 (2009), 3020–3029  crossref  mathscinet  zmath  isi
    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  crossref  zmath  isi
    7. Punzo F., “Phragmèn-Lindelöf principles for fully nonlinear elliptic equations with unbounded coefficients”, Commun. Pure Appl. Anal., 9:5 (2010), 1439–1461  crossref  mathscinet  zmath  isi
    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  crossref  mathscinet  zmath  isi
    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  crossref  mathscinet  zmath  isi
    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  crossref  mathscinet  zmath  isi
    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  crossref  mathscinet  zmath  isi  elib
    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  crossref  mathscinet  zmath  isi
    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  crossref  mathscinet  zmath  isi  elib
    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  crossref  mathscinet  zmath  adsnasa  isi
    15. Kamin Sh., Punzo F., “Prescribed Conditions At Infinity For Parabolic Equations”, Commun. Contemp. Math., 17:1 (2015), 1450004  crossref  mathscinet  zmath  isi
    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  crossref  mathscinet  zmath  adsnasa  isi
    17. Kamin Sh., Punzo F., “Dirichlet conditions at infinity for parabolic and elliptic equations”, Nonlinear Anal.-Theory Methods Appl., 138 (2016), 156–175  crossref  mathscinet  zmath  isi  scopus
    18. Punzo F., Strani M., “Dirichlet Boundary Conditions For Degenerate and Singular Nonlinear Parabolic Equations”, Potential Anal., 47:2 (2017), 151–168  crossref  mathscinet  zmath  isi  scopus
    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  mathscinet  zmath  isi
    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  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  isi
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