Regularity properties of integral problems for wave equations and applications

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Advances in the Theory of Nonlinear Analysis and its Application
Volume:7 Issue:1
Regularity properties of integral problems for wave equations and applications

Regularity properties of integral problems for wave equations and applications

Authors : Veli SHAKHMUROV, Rishad SHAHMUROV

Pages : 82-102

Doi:10.31197/atnaa.1200398

View : 75 | Download : 129

Publication Date : 2023-03-31

Article Type : Research Paper

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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