Regularity properties of integral problems for wave equations and applications

Year 2023, Volume: 7 Issue: 1, 82 - 102, 31.03.2023

Veli Shakhmurov , Rishad Shahmurov

https://doi.org/10.31197/atnaa.1200398

Cited By: 1

Abstract

In this paper, the integral problem for linear and nonlinear wave equations are studied.The equation involves elliptic operator L and abstract operator A in Hilbert space H. Here, assuming enough smoothness on the initial data given in corresponding interpolation spaces and operators the existence, uniqueness, L^{p}-regularity properties to solutions are established. By choosing the space H and operators L, A, the regularity properties to solutions of different classes of wave equations in the field of physics are obtained.

Keywords

Apstract differential equations, Wave equations, Operator theory, $L^{p}$-regularity property of solutions, Fourier multipliers

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