Regularity properties of integral problems for wave equations and applications

Yıl 2023, Cilt: 7 Sayı: 1, 82 - 102, 31.03.2023

Veli Shakhmurov Rishad Shahmurov

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

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