Nonexistence of Global Solutions to Double Dispersion Equations with Linear Restoring Force and Nonlinearities with Variable Coefficients

Authors

  • Natalia Kolkovska Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
  • Milena Dimova University of National and World Economy, Bulgaria and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
  • Nikolay Kutev Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

DOI:

https://doi.org/10.7546/CRABS.2023.10.02

Keywords:

double dispersion equations, linear restoring force, finite time blow up, nonlinearities with variable coefficients

Abstract

We investigate Cauchy problem to double dispersion equations with polynomial type nonlinearities with variable coefficients. Necessary and sufficient conditions for nonexistence of global weak solutions and nonblowing up ones are found for subcritical initial energy. For supercritical energy a sufficient condition for finite time blow up of the weak solutions, independent of the scalar product of the initial data, is developed.

Author Biographies

Natalia Kolkovska, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

Mailing Address:
Institute of Mathematics and Informatics,
Bulgarian Academy of Sciences
Akad. G. Bonchev St, Bl. 8
1113 Sofia, Bulgaria

E-mail: natali@math.bas.bg

Milena Dimova, University of National and World Economy, Bulgaria and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

Mailing Address:
University of National and World Economy
19 8th December St
1700 Sofia, Bulgaria

and

Institute of Mathematics and Informatics,
Bulgarian Academy of Sciences
Akad. G. Bonchev St, Bl. 8
1113 Sofia, Bulgaria

E-mail: mdimova@unwe.bg

Nikolay Kutev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

Mailing Address:
Institute of Mathematics and Informatics,
Bulgarian Academy of Sciences
Akad. G. Bonchev St, Bl. 8
1113 Sofia, Bulgaria

E-mail: kutev@math.bas.bg

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Published

31-10-2023

How to Cite

[1]
N. Kolkovska, M. Dimova, and N. Kutev, “Nonexistence of Global Solutions to Double Dispersion Equations with Linear Restoring Force and Nonlinearities with Variable Coefficients”, C. R. Acad. Bulg. Sci., vol. 76, no. 10, pp. 1486–1494, Oct. 2023.

Issue

Vol. 76 No. 10 (2023)

Section

Mathematics

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