On the Absence of Weak Solutions of Nonlinear Nonnegative Higher Order Parabolic Inequalities with a Nonlocal Source

Capa

Citar

Texto integral

Acesso aberto Acesso aberto
Acesso é fechado Acesso está concedido
Acesso é fechado Somente assinantes

Resumo

The paper proves the absence of solutions of semilinear parabolic inequalities and higher order systems with a singular potential and nonlocal sources. The proofs are based on the test function method developed by E. Mitidieri and S.I. Pokhozhaev.

Sobre autores

V. Admasu

RUDN University

Autor responsável pela correspondência
Email: mihretesme@gmail.com
117198, Moscow, Russia

Bibliografia

  1. Митидиери Э., Похожаев С.И. Отсутствие положительных решений для квазилинейных эллиптических задач в // Тр. Матем. ин-та им. В.А. Стеклова. 1999. Т. 227. С. 186–216.
  2. Mitidieri E., Pohozaev S.I. Nonexistence of weak solutions for some degenerate elliptic and parabolic problems on // J. Evolut. Equat. 2001. V. 1. № 2. P. 189–220.
  3. Kartsatos A.G., Kurta V.V. On the critical Fujita exponents for solutions of quasilinear parabolic inequalities // J. Math. Anal. Appl. 2002. V. 269. № 1. P. 73–86.
  4. Jiang Z.X., Zheng, S.N. A Liouville-type theorem for a doubly degenerate parabolic inequality // Acta Math. Scientia. 2010. V. 30. № 3. P. 639–643.
  5. Admasu W.E., Galakhov E.I., Salieva O.A. Nonexistence of nontrivial weak solutions of some nonlinear inequalities with gradient nonlinearity // Contemporary Math. Fundament. Direct. 2021. V. 67. № 1. P. 1–13.
  6. Галахов Е.И. Об отсутствии локальных решений некоторых эволюционных задач // Матем. заметки. 2009. Т. 86. № 3. С. 337–349.
  7. Yang C., Zhao L., Zheng S. The critical Fujita exponent for the fast diffusion equation with potential // J. Math. Anal. Appl. 2013. V. 398. № 2. P. 879–885.
  8. Liu C. The critical Fujita exponent for a diffusion equation with a potential term // Lithuanian Math. J. 2014. V. 54. № 2. P. 182–191.
  9. Ishige K. On the Fujita exponent for a semilinear heat equation with a potential term // J. Math. Anal. Appl. 2008. V. 344. № 1. P. 231–237.
  10. Pinsky R. The Fujita exponent for semilinear heat equations with quadratically decaying potential or in an exterior domain // J. Diff. Eq. 2009. V. 246. № 6. P. 2561–2576.
  11. Chen C.S., Huang J.C. Some nonexistence results for degenerate parabolic inequalities with local and nonlocal nonlinear terms // J. Nanjing Univ. Math. Biq. 2004. V. 21. № 1. P. 12–20.
  12. Xiao S., Fang Z.B. Nonexistence of solutions for the quasilinear parabolic differential inequalities with singular potential term and nonlocal source // J. Ineq. Appl. 2020. V. 2020. № 1. P. 1–9.
  13. Галахов Е.И. Об эллиптических и параболических неравенствах высокого порядка с особенностями на границе // Тр. Матем. ин-та им. В.А. Стеклова. 2010. Т. 269. № 1. С. 76–84.

Arquivos suplementares

Arquivos suplementares
Ação
1. JATS XML

Declaração de direitos autorais © В.Е. Адмасу, 2023