Abstract

This paper is devoted to the study of a nonlinear wave equation with initial conditions and nonlocal boundary conditions of 2N‐point type, which connect the values of an unknown function u(x,t)  at x = 1, x = 0,  x = ηi(t), and x = θi(t), where 0<𝜂1(𝑡)<𝜂2(𝑡)<…<𝜂𝑁−1(𝑡)<1,   0<𝜃1(𝑡)<𝜃2(𝑡)<…<𝜃𝑁−1(𝑡)<1,   for all t ≥ 0.  First, we prove local existence of a unique weak solution by using density arguments and applying the Banach's contraction principle. Next, under the suitable conditions, we show that the problem considered has a unique global solution u(t)  with energy decaying exponentially as t → +∞. Finally, we present numerical results.