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 sąlyga Iškilių hamiltonianų atveju yra užduotos formules Koši uždavinių sprendiniams: pirmosios lygties atveju, kai ϕ(x) yra pusiau tolydi iš apačios ir antrosios lygties atveju pradinė funkcija tolydi Lipšico prasme ir yra laužtė, trečiosios lygties atveju pradinė funkcija aprėžta ir dalimis pastovi.
Gudynas, G. (2001). On representation formula for solutions of Hamilton‐Jacobi equation for some types of initial conditions. Mathematical Modelling and Analysis, 6(2), 241-250. https://doi.org/10.3846/13926292.2001.9637163
Authors who publish with this journal agree to the following terms
that this article contains no violation of any existing copyright or other third party right or any material of a libelous, confidential, or otherwise unlawful nature, and that I will indemnify and keep indemnified the Editor and THE PUBLISHER against all claims and expenses (including legal costs and expenses) arising from any breach of this warranty and the other warranties on my behalf in this agreement;
that I have obtained permission for and acknowledged the source of any illustrations, diagrams or other material included in the article of which I am not the copyright owner.
on behalf of any co-authors, I agree to this work being published in the above named journal, Open Access, and licenced under a Creative Commons Licence, 4.0 https://creativecommons.org/licenses/by/4.0/legalcode. This licence allows for the fullest distribution and re-use of the work for the benefit of scholarly information.
For authors that are not copyright owners in the work (for example government employees), please contact VILNIUS TECHto make alternative agreements.
