Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 44, Issue 1, Pages 668-692Publisher
WILEY
DOI: 10.1002/mma.6773
Keywords
boundary conditions of 2N-point type; exponential decay; global existence; local existence; nonlinear wave equation
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Funding
- Vietnam National University HoChiMinh City (VNU-HCM) [B2020-18-01]
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This paper focuses on a nonlinear wave equation with initial conditions and nonlocal boundary conditions, proving the existence of a unique weak solution and a unique global solution under certain conditions, with the solution exhibiting exponential energy decay as t approaches positive infinity.
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 functionu(x,t) atx = 1,x = 0, x = eta(i)(t), andx = theta(i)(t),where0= 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 solutionu(t) with energy decaying exponentially ast -> +infinity. Finally, we present numerical results.
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