Nonexistence of solutions to Cauchy problems for anisotropic pseudoparabolic equations

Abstract

We study the nonexistence of nonnegative global weak solutions to the Cauchy problem of anisotropic pseudoparabolic equations and corresponding systems. Using the method of nonlinear capacity, we establish the sufficient conditions for the nonexistence of gobal weak solutions. The result is extended to the case of coupled system of the same type of equations.

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Correspondence to Birilew Belayneh Tsegaw.

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I testify that my article submitted to Journal of Elliptic and Parabolic equations entitled by “Nonexistence of Solutions to Cauchy Problems for Anisotropic Pseudo-parabolic Equations” ensure the following professional ethics: (1) this manuscript is not currently being considered for publication in another journals; (2) this manuscript is original and has not been published elsewhere in any form or language in whole or in part; (3) the result of this manuscript is clearly presented without fabrication and not a split of other published works; (4) as an author, I am responsible for its content.

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Tsegaw, B.B. Nonexistence of solutions to Cauchy problems for anisotropic pseudoparabolic equations. J Elliptic Parabol Equ 6, 919–934 (2020). https://doi.org/10.1007/s41808-020-00087-5

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Keywords

  • Anisotropic pseudoparabolic equation
  • System of anisotropic pseudoparabolic equations
  • Nonexistence of solutions
  • Nonlinear capacity method
  • Test functions

Mathematics Subject Classification

  • 35K30
  • 35K46
  • 35K70