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2003 | 1 | 1 | 61-78
Tytuł artykułu

Existence and nonexistence results for reaction-diffusion equations in product of cones

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Problems of existence and nonexistence of global nontrivial solutions to quasilinear evolution differential inequalities in a product of cones are investigated. The proofs of the nonexistence results are based on the test-function method developed, for the case of the whole space, by Mitidieri, Pohozaev, Tesei and Véron. The existence result is established using the method of supersolutions.
Wydawca
Czasopismo
Rocznik
Tom
1
Numer
1
Strony
61-78
Opis fizyczny
Daty
wydano
2003-03-01
online
2003-03-01
Twórcy
Bibliografia
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  • [12] G.G. Laptev, Nonexistence of solutions for parabolic inequalities in unbounded cone-like domains via the test function method, J. Evolution Equations. 2002 (in press)
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  • [17] E. Mitidieri, S.I. Pohozaev, Nonexistence of global positive solutions to quasilinear elliptic inequalities, Dokl. Russ. Acad. Sci., Vol. 57 (1998), 250–253.
  • [18] E. Mitidieri, S.I. Pohozaev, Nonexistence of positive solutions for a system of quasilinear elliptic equations and inequalities in ℝn , Dokl. Russ. Acad. Sci., Vol. 59 (1999), 1351–1355.
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  • [20] E. Mitidieri, S.I. Pohozaev, Nonexistence of weak solutions for some degenerate elliptic and parabolic problems on ℝn , J. Evolution Equations, Vol. 1 (2001), 189–220. http://dx.doi.org/10.1007/PL00001368
  • [21] E. Mitidieri, S.I. Pohozaev, Nonexistence of weak solutions for some degenerate and singular hyperbolic problems on ℝn , Proc. Steklov Inst. Math., Vol. 232 (2001), 240–259.
  • [22] E. Mitidieri, S.I. Pohozaev, A priori Estimates and Nonexistence of Solutions to Nonlinear Partial Differential Equations and Inequalities, Moscow, Nauka, 2001. (Proc. Steklov Inst. Math., Vol. 234).
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  • [25] S.I. Pohozaev, A. Tesei, Blow-up of nonnegative solutions to quasilinear parabolic inequalities, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., Vol. 11 (2000), 99–109.
  • [26] S.I. Pohozaev, A. Tesei, Critical exponents for the absence of solutions for systems of quasilinear parabolic inequalities, Differ. Uravn., Vol. 37 (2001), 521–528.
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  • [32] G. N. Watson, A treatise on the Theory of Bessel Functions, Cambridge University Press, London/New York, 1966.
  • [33] Qi Zhang, Blow-up results for nonlinear parabolic equations on manifolds, Duke Math. J., Vol. 97 (1999), 515–539. http://dx.doi.org/10.1215/S0012-7094-99-09719-3
  • [34] Qi Zhang, The quantizing effect of potentials on the critial number of reaction-diffusion equations, J. Differential Equations, Vol. 170 (2001), 188–214. http://dx.doi.org/10.1006/jdeq.2000.3815
  • [35] Qi Zhang, Global lower bound for the heat kernel of \( - \Delta + \frac{c}{{|x|^2 }}\) , Proc. Amer. Math. Soc., Vol. 129 (2001), 1105–1112. http://dx.doi.org/10.1090/S0002-9939-00-05757-9
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475664
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