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Doklady Mathematics

, Volume 98, Issue 3, pp 555–558 | Cite as

The Existence and Behavior of Global Solutions to a Mixed Problem with Acoustic Transmission Conditions for Nonlinear Hyperbolic Equations with Nonlinear Dissipation

  • A. B. AlievEmail author
  • S. E. Isayeva
Mathematics
  • 4 Downloads

Abstract

A mixed problem with acoustic transmission conditions for nonlinear hyperbolic equations with nonlinear dissipation is considered. The existence, uniqueness, and exponential decay of global solutions to this problem with focusing nonlinear sources are proved Additionally, the existence of global solutions and the solution blow-up in a finite time are proved for the case of defocusing nonlinear sources.

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Institute of Mathematics and MechanicsNational Academy of Sciences of AzerbaijanBakuAzerbaijan
  2. 2.Azerbaijan Technical UniversityBakuAzerbaijan
  3. 3.Baku State UniversityBakuAzerbaijan

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