- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 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 : 64 | Download : 120
Publication Date : 2023-03-31
Article Type : Research Article
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