Existence of Solutions for One-dimensional Wave Equations with Nonlocal Conditions

By Sergei A. Beilin. 2001

119 citations recorded by the source corpus.

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Citations in the corpus

On the solution of an initial‐boundary value problem that combines Neumann and integral condition for the wave equation (2005, background): “Beilin [28] investigated the nonlocal analogue to classical mixed problems, which involve initial, boundary integral conditions.”
A nonlinear nonlocal mixed problem for a second order pseudoparabolic equation (2006, background): “References [1] S.A. Beilin, Existence of solutions for one-dimensional wave equation with nonlocal conditions, Ele J. Differential Equations 76 (2001) 1–8.”
The use of cubic B‐spline scaling functions for solving the one‐dimensional hyperbolic equation with a nonlocal conservation condition (2007, methodology): “The proof of the existence, uniqueness, and continuous dependence of a strong solution upon the data, for the current model is studied in Bouziani [16].”
A numerical method for the wave equation subject to a non-local conservation condition (2006, background): “Beilin [2] and Kavalloris and Tzanetis [9]), relatively few papers give the numerical solutions of such problems.”
Combined finite difference and spectral methods for the numerical solution of hyperbolic equation with an integral condition (2008, background): “For existence and uniqueness of the solution and some applications the interested readers can see [6, 9–16].”
Numerical solution of the one‐dimensional wave equation with an integral condition (2007, background): “Beilin [3] investigated the nonlocal analogue to classical mixed problems, which involve initial, boundary integral conditions.”