Veli Shakhmurov and Rishad Shahmurov
Nonlocal Boussinesq Equations in Vector Valued Spaces and Applications
Dynamic Systems and Applications 34 (2025)   165-188

https://doi.org/10.46719/dsa2025.34.09

ABSTRACT.
In this paper, the Cauchy problem for linear and nonlinear nonlocal Boussinesq equations is studied. The equation involves convolution terms including abstract operator functions in Fourier type Banach space E. Here, assuming enough smoothness on the initial data and the growth assumptions on operator functions, the local, global existence, uniqueness and regularity properties of solutions are established in terms of fractional powers of given sectorial operator. We can obtain a different classes of nonlocal Boussinesq equations by choosing the space E and linear operator, which occur in a wide variety of physical systems.

AMS (MOS) Subject Classification. 35Axx, 35L90, 47B25, 35L20, 46E40.

Key Words and Phrases. Nonlocal wave equations, Fourier type Banach spaces, Boussinesq equations, Abstract differential equations, Fourier multipliers