On representation formula for solutions of Hamilton‐Jacobi equation for some types of initial conditions
This article investigates the representation formula for the semiconcave solutions of the Cauchy problem for Hamilton‐Jacobi equation with the convex Hamiltonian and the unbounded lower semicontinous initial function. The formula like Hopf ‘s formula is given by forming envelope of some fundamental...
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Vilnius Gediminas Technical University
2001-12-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/9910 |
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doaj-2b48d9d526ab4e89a671773b3772eec52021-07-02T14:19:46ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102001-12-016210.3846/13926292.2001.9637163On representation formula for solutions of Hamilton‐Jacobi equation for some types of initial conditionsG. Gudynas0Department of System Research , Klaipeda University , H. Manto 84, Klaipeda, LT‐58008 This article investigates the representation formula for the semiconcave solutions of the Cauchy problem for Hamilton‐Jacobi equation with the convex Hamiltonian and the unbounded lower semicontinous initial function. The formula like Hopf ‘s formula is given by forming envelope of some fundamental solutions of the equation. Apie Hamiltono-Jakobo sprendinių išraiškas tam tikroms pradinėms sąlygoms Santrauka Nagrinėjami Kosi uždaviniai lygtims su pradine salyga Iškiliu hamiltonianu atveju yra užduotos formules Koši uždaviniu sprendiniams: pirmosios lygties atveju, kai ϕ(x) yra pusiau tolydi iš apačios ir antrosios lygties atveju pradine funkcija tolydi Lipšico prasme ir yra laužte, trečiosios lygties atveju pradine funkcija aprežta ir dalimis pastovi. First Published online: 14 Oct 2010 https://journals.vgtu.lt/index.php/MMA/article/view/9910- |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
G. Gudynas |
| spellingShingle |
G. Gudynas On representation formula for solutions of Hamilton‐Jacobi equation for some types of initial conditions Mathematical Modelling and Analysis - |
| author_facet |
G. Gudynas |
| author_sort |
G. Gudynas |
| title |
On representation formula for solutions of Hamilton‐Jacobi equation for some types of initial conditions |
| title_short |
On representation formula for solutions of Hamilton‐Jacobi equation for some types of initial conditions |
| title_full |
On representation formula for solutions of Hamilton‐Jacobi equation for some types of initial conditions |
| title_fullStr |
On representation formula for solutions of Hamilton‐Jacobi equation for some types of initial conditions |
| title_full_unstemmed |
On representation formula for solutions of Hamilton‐Jacobi equation for some types of initial conditions |
| title_sort |
on representation formula for solutions of hamilton‐jacobi equation for some types of initial conditions |
| publisher |
Vilnius Gediminas Technical University |
| series |
Mathematical Modelling and Analysis |
| issn |
1392-6292 1648-3510 |
| publishDate |
2001-12-01 |
| description |
This article investigates the representation formula for the semiconcave solutions of the Cauchy problem for Hamilton‐Jacobi equation with the convex Hamiltonian and the unbounded lower semicontinous initial function. The formula like Hopf ‘s formula is given by forming envelope of some fundamental solutions of the equation.
Apie Hamiltono-Jakobo sprendinių išraiškas tam tikroms pradinėms sąlygoms
Santrauka
Nagrinėjami Kosi uždaviniai lygtims su pradine salyga Iškiliu hamiltonianu atveju yra užduotos formules Koši uždaviniu sprendiniams: pirmosios lygties atveju, kai ϕ(x) yra pusiau tolydi iš apačios ir antrosios lygties atveju pradine funkcija tolydi Lipšico prasme ir yra laužte, trečiosios lygties atveju pradine funkcija aprežta ir dalimis pastovi.
First Published online: 14 Oct 2010
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https://journals.vgtu.lt/index.php/MMA/article/view/9910 |
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