We introduce new reproducing kernel Hilbert spaces on a semi-infinite domain and demonstrate existence and uniqueness of solutions to the nonhomogeneous telegraph equation in these spaces if the driver is square-integrable and sufficiently smooth.
We introduce new reproducing kernel Hilbert spaces on a trapezoidal
semi-infinite domain $B_{\infty}$ in the plane. We
establish uniform approximation results in terms of the number of nodes
on compact subsets of $B_{\infty}$ for solutions to
nonhomogeneous hyperbolic partial differential equations in one of these
spaces,
$\widetilde{W}(B_{\infty})$.
Furthermore, we demonstrate the stability of such solutions with respect
to the driver. Finally, we give an example to illustrate the efficiency
and accuracy of our results.
We use the contraction mapping theorem to present the existence and uniqueness of solutions in a short time to a system of non-linear Volterra integral equations in a certain type of direct-sum H[a; b] of a Hilbert space V[a; b]. We extend the local existence and uniqueness of solutions to the global existence and uniqueness of solutions to the proposed problem. Because the kernel function is a transcendental function in H[a; b] on the interval [a; b], the results are novel and very important in numerical approximation.
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