Existence local and global solution of multipoint Cauchy problem for nonlocal nonlinear equations

2019/03/01 by Shakhmurov, Veli, Shahmurov, Rishad
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.01553

Abstract

In this paper, the multipoint Cauchy problem for nonlocal nonlinear wave type equatıons are studied.The equation involves a convolution integral operator with a general kernel function whose Fourier transform is nonnegative. We establish local and global existence and uniqueness of solutions assuming enough smoothness on the initial data together with some growth conditions on the nonlinear term

Related

• Nonlocal Cauchy problems for wave equations and applications
• The regularity properties of nonlocal abstract wave equations
• Multipoint Cauchy problem for nonlinear wave equations in vector-valued spaces
• Finite time blow-up for a wave equation with a nonlocal nonlinearity
• The regularity properties and blow-up for convolution wave equations and applications