Nonlocal Cauchy problems for wave equations and applications

2017/07/13 by Veli Shakhmurov, Shakhmurov, Veli
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1707.04492

openalex publication_date 2017/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, the existence, the uniqueness and estimates of solution to the integral Cauchy problem for linear and nonlinear abstract wave equations are proved. The equation includes a linear operator A defined in a Banach space E, in which by choosing E and A we can obtain numerous classis of nonlocal initial value problems for wave equations which occur in a wide variety of physical systems.

Citations

• On the regularity properties of a model problem related to wave maps

Related

• The regularity properties of nonlocal abstract wave equations
• Multipoint Cauchy problem for nonlinear wave equations in vector-valued spaces
• Existence local and global solution of multipoint Cauchy problem for nonlocal nonlinear equations
• The Cauchy Problem for Wave Equations with NonLipschitz Coefficients
• Well-posedness and inverse problems for semilinear nonlocal wave equations