Representation Formula for Solutions of Eikonal Type Equations
Equations of an eikonal type ones arise in many areas of applications, including optics, fluid mechanics, material sciences, and control theory. This article investigates the representation formula for semiconcave solutions of the boundary problem for eikonal type equation. The formula is given by f...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2001-06-01
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| Series: | Nonlinear Analysis |
| Subjects: | |
| Online Access: | http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/15225 |
| _version_ | 1828301261193084928 |
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| author | Gintautas Gudynas |
| author_facet | Gintautas Gudynas |
| author_sort | Gintautas Gudynas |
| collection | DOAJ |
| description | Equations of an eikonal type ones arise in many areas of applications, including optics, fluid mechanics, material sciences, and control theory. This article investigates the representation formula for semiconcave solutions of the boundary problem for eikonal type equation. The formula is given by forming envelope of some fundamental solutions of the equation. Using these fundamental solutions we obtain the representation formula for solutions of Cauchy problem for appropriate Hamilton – Jacobi equation. |
| first_indexed | 2024-04-13T13:20:57Z |
| format | Article |
| id | doaj.art-ad70e5b4ab55485eb59eb90ea9dbc4a4 |
| institution | Directory Open Access Journal |
| issn | 1392-5113 2335-8963 |
| language | English |
| last_indexed | 2024-04-13T13:20:57Z |
| publishDate | 2001-06-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj.art-ad70e5b4ab55485eb59eb90ea9dbc4a42022-12-22T02:45:19ZengVilnius University PressNonlinear Analysis1392-51132335-89632001-06-016110.15388/NA.2001.6.1.15225Representation Formula for Solutions of Eikonal Type EquationsGintautas Gudynas0Klaipėda University, LithuaniaEquations of an eikonal type ones arise in many areas of applications, including optics, fluid mechanics, material sciences, and control theory. This article investigates the representation formula for semiconcave solutions of the boundary problem for eikonal type equation. The formula is given by forming envelope of some fundamental solutions of the equation. Using these fundamental solutions we obtain the representation formula for solutions of Cauchy problem for appropriate Hamilton – Jacobi equation.http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/15225EikonalHamilton – Jacobisemiconcave solution |
| spellingShingle | Gintautas Gudynas Representation Formula for Solutions of Eikonal Type Equations Nonlinear Analysis Eikonal Hamilton – Jacobi semiconcave solution |
| title | Representation Formula for Solutions of Eikonal Type Equations |
| title_full | Representation Formula for Solutions of Eikonal Type Equations |
| title_fullStr | Representation Formula for Solutions of Eikonal Type Equations |
| title_full_unstemmed | Representation Formula for Solutions of Eikonal Type Equations |
| title_short | Representation Formula for Solutions of Eikonal Type Equations |
| title_sort | representation formula for solutions of eikonal type equations |
| topic | Eikonal Hamilton – Jacobi semiconcave solution |
| url | http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/15225 |
| work_keys_str_mv | AT gintautasgudynas representationformulaforsolutionsofeikonaltypeequations |