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

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

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.

About the authors

V. E. Admasu

RUDN University

Author for correspondence.
Email: mihretesme@gmail.com
117198, Moscow, Russia

References

  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.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2023 В.Е. Адмасу