Goursat problem for loaded degenerate second order hyperbolic equation with Gellerstedt operator in principal part
In the paper we study a loaded degenerate hyperbolic equation of the second order with variable coefficients. The principal part of the equation is the Gellerstedt operator. The loaded term is given in the form of the trace of desired solution on the degenerate line. The latter is located in the inn...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Samara State Technical University
2016-03-01
|
| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| Subjects: | |
| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/20457/16704 |
| _version_ | 1818277868640141312 |
|---|---|
| author | Anatoly H Attaev |
| author_facet | Anatoly H Attaev |
| author_sort | Anatoly H Attaev |
| collection | DOAJ |
| description | In the paper we study a loaded degenerate hyperbolic equation of the second order with variable coefficients. The principal part of the equation is the Gellerstedt operator. The loaded term is given in the form of the trace of desired solution on the degenerate line. The latter is located in the inner part of the domain. We investigate a boundary value problem. The boundary conditions are given on a characteristics line of the equation under study. For the model equation (when all subordinated coefficients are zero) we construct an explicit representation for solution of the Goursat problem. In the general case, we reduce the problem to an integral Volterra equation of the second kind. We apply the method realized by Sven Gellerstedt solving the second Darboux problem. In both cases, model and general, we use widely properties of the Green-Hadamard function. |
| first_indexed | 2024-12-12T23:08:23Z |
| format | Article |
| id | doaj.art-f7420e45b8164540be39737f722e0233 |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-12-12T23:08:23Z |
| publishDate | 2016-03-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-f7420e45b8164540be39737f722e02332022-12-22T00:08:39ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812016-03-0120172110.14498/vsgtu145217877Goursat problem for loaded degenerate second order hyperbolic equation with Gellerstedt operator in principal partAnatoly H Attaev0Institute of Applied Mathematics and AutomationIn the paper we study a loaded degenerate hyperbolic equation of the second order with variable coefficients. The principal part of the equation is the Gellerstedt operator. The loaded term is given in the form of the trace of desired solution on the degenerate line. The latter is located in the inner part of the domain. We investigate a boundary value problem. The boundary conditions are given on a characteristics line of the equation under study. For the model equation (when all subordinated coefficients are zero) we construct an explicit representation for solution of the Goursat problem. In the general case, we reduce the problem to an integral Volterra equation of the second kind. We apply the method realized by Sven Gellerstedt solving the second Darboux problem. In both cases, model and general, we use widely properties of the Green-Hadamard function.https://journals.eco-vector.com/1991-8615/article/viewFile/20457/16704goursat problemloaded equationhyperbolic equationdegenerate equationgellerstedt operatorthe green-hadamard's function method |
| spellingShingle | Anatoly H Attaev Goursat problem for loaded degenerate second order hyperbolic equation with Gellerstedt operator in principal part Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki goursat problem loaded equation hyperbolic equation degenerate equation gellerstedt operator the green-hadamard's function method |
| title | Goursat problem for loaded degenerate second order hyperbolic equation with Gellerstedt operator in principal part |
| title_full | Goursat problem for loaded degenerate second order hyperbolic equation with Gellerstedt operator in principal part |
| title_fullStr | Goursat problem for loaded degenerate second order hyperbolic equation with Gellerstedt operator in principal part |
| title_full_unstemmed | Goursat problem for loaded degenerate second order hyperbolic equation with Gellerstedt operator in principal part |
| title_short | Goursat problem for loaded degenerate second order hyperbolic equation with Gellerstedt operator in principal part |
| title_sort | goursat problem for loaded degenerate second order hyperbolic equation with gellerstedt operator in principal part |
| topic | goursat problem loaded equation hyperbolic equation degenerate equation gellerstedt operator the green-hadamard's function method |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/20457/16704 |
| work_keys_str_mv | AT anatolyhattaev goursatproblemforloadeddegeneratesecondorderhyperbolicequationwithgellerstedtoperatorinprincipalpart |