Existence of Unique Solutions to the Telegraph Equation in Binary Reproducing Kernel Hilbert Spaces
We demonstrate the existence of a unique solution to a nonhomogeneous telegraph initial/boundary value problem on the unit square in an appropriate binary reproducing kernel Hilbert space which depends on the smoothness of the driver. Examples are given to illustrate the numerical effectiveness of the reproducing kernel method when properly applied and the aberrations which can occur when no solution exists in the space.
A. Akgul and D. E. Grow, "Existence of Unique Solutions to the Telegraph Equation in Binary Reproducing Kernel Hilbert Spaces," Differential Equations and Dynamical Systems, vol. 28, pp. 715-744, Springer, Jul 2020.
The definitive version is available at https://doi.org/10.1007/s12591-019-00453-3
Mathematics and Statistics
Keywords and Phrases
Existence of solutions; Reproducing kernel Hilbert space; Telegraph equation
International Standard Serial Number (ISSN)
Article - Journal
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01 Jul 2020