Geodesic
Existence of solutions to a one-dimensional Hamilton–Jacobi equation with a degenerate Hamiltonian
Tomasz Cieślak 1   ; Hiroshi Wakui 2
1 Institute of Mathematics Polish Academy of Sciences 00-656 Warszawa, Poland <a href="https://orcid.org/0000-0003-4191-4231">ORCID: 0000-0003-4191-4231</a>
2 Mathematical Institute University of Wrocław pl. Grunwaldzki 2/4 50-384 Wrocław, Poland and Faculty of Science Division I Tokyo University of Science Tokyo 162-8601, Japan
Applicationes Mathematicae, Tome 47 (2020) no. 2, pp. 155-163 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study a one-dimensional Hamilton–Jacobi initial value problem for a degenerate Hamiltonian occurring in multipeakon dynamics. Such a degenerate problem does not obey the usual viscosity solutions theory; viability type extensions do not seem to cover it either. Thanks to a particular change of variables, we reduce the problem to the case where Hopf theory is sufficient. Moreover, we show that our solutions are solutions in the viscosity sense.
DOI : 10.4064/am2407-7-2020
Keywords: study one dimensional hamilton jacobi initial value problem degenerate hamiltonian occurring multipeakon dynamics degenerate problem does obey usual viscosity solutions theory viability type extensions seem cover either thanks particular change variables reduce problem where hopf theory sufficient moreover solutions solutions viscosity sense

Tomasz Cieślak  1   ; Hiroshi Wakui  2

1 Institute of Mathematics Polish Academy of Sciences 00-656 Warszawa, Poland <a href="https://orcid.org/0000-0003-4191-4231">ORCID: 0000-0003-4191-4231</a>
2 Mathematical Institute University of Wrocław pl. Grunwaldzki 2/4 50-384 Wrocław, Poland and Faculty of Science Division I Tokyo University of Science Tokyo 162-8601, Japan 
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     author = {Tomasz Cie\'slak and Hiroshi Wakui},
     title = {Existence of solutions to a one-dimensional {Hamilton{\textendash}Jacobi} equation with a degenerate {Hamiltonian}},
     journal = {Applicationes Mathematicae},
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Tomasz Cieślak; Hiroshi Wakui. Existence of solutions to a one-dimensional Hamilton–Jacobi equation with a degenerate Hamiltonian. Applicationes Mathematicae, Tome 47 (2020) no. 2, pp. 155-163. doi: 10.4064/am2407-7-2020

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