Turkish Journal of Mathematics
Author ORCID Identifier
SVETLIN GEORGIEV: 0000-0001-8015-4226
JERVIN ZEN LOBO: 0000-0002-3224-8049
SANKET TIKARE: 0000-0002-9000-3031
Abstract
In this paper, we obtain the canonical form of second-order linear partial dynamic equations in two independent variables on time scales, together with the identity for the characteristic quadratic form. This is then used to classify these equations as hyperbolic, elliptic, or parabolic. We deduce the characteristic equations in each case, determine their roots, and provide the corresponding characteristic curves. In one case, we derive the generalized Beltrami equations on time scales. Suitable examples involving equations of interest are explored, and the developed theory is illustrated through these examples.
DOI
10.55730/1300-0098.3683
Keywords
Canonical forms, elliptic equations, hyperbolic equations, parabolic equations, partial dynamic equations, time scales
First Page
820
Last Page
841
Publisher
The Scientific and Technological Research Council of Türkiye (TÜBİTAK)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
GEORGIEV, S. G, LOBO, J, & TIKARE, S (2026). Analysis and categorization of second-order linear partial dynamic equations on time scales. Turkish Journal of Mathematics 50 (4): 820-841. https://doi.org/10.55730/1300-0098.3683
