Keywords and Phrases
Differential operator; Existence and uniqueness; Reproducing kernel Hilbert spaces; Stability of solution; Telegraph operator
"We introduce new reproducing kernel Hilbert spaces W2(m,n) (D) on unbounded plane regions D. We study linear non-homogeneous hyperbolic partial differential equation problems on D with solutions in various reproducing kernel Hilbert spaces. We establish existence and uniqueness results for such solutions under appropriate hypotheses on the driver. Stability of solutions with respect to the driver is analyzed and local uniform approximation results are obtained which depend on the density of nodes. The local uniform approximation results required a careful determination of the reproducing kernel Hilbert spaces on which the elementary differential operators ∂/∂x and ∂/∂t are bounded. We apply these findings to second order hyperbolic partial differential equations to assist us in demonstrating the aforementioned local uniform approximation results. Finally, we illustrate the efficiency and effectiveness of our theoretical investigations with several numerical examples"--Abstract, page iv.
Grow, David E.
Clark, Stephen L.
Gelles, Gregory M.
Mathematics and Statistics
Ph. D. in Mathematics
Missouri University of Science and Technology
Journal article titles appearing in thesis/dissertation
- Boundedness of differential operators on binary reproducing kernel Hilbert spaces
- New reproducing kernel Hilbert spaces on semi-infinite domains with existence and uniqueness results for the non-homogeneous telegraph equation
- Stability and approximation of solutions in new reproducing kernel Hilbert spaces on a semi-infinite domain
x, 91 pages
© 2019 Jabar Salih Hassan, All rights reserved.
Dissertation - Open Access
Hassan, Jabar S., "New reproducing kernel Hilbert spaces on plane regions, their properties, and applications to partial differential equations" (2019). Doctoral Dissertations. 2992.