具有退化哈密顿量的一维哈密顿-雅可比方程解的存在性

Q4 Mathematics

Applicationes Mathematicae Pub Date : 2020-01-01 DOI:10.4064/am2407-7-2020

Tomasz Cieślak, H. Wakui

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引用次数: 3

摘要

研究了多峰动力学中退化哈密顿量的一维Hamilton-Jacobi初值问题。这种退化问题不服从通常的粘度解理论;可行性类型扩展似乎也没有涵盖它。由于变量的特殊变化，我们将问题简化为Hopf理论是充分的。此外，我们证明了我们的解是粘度意义上的解。

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Existence of solutions to a one-dimensional Hamilton–Jacobi equation with a degenerate Hamiltonian

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.

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来源期刊

Applicationes Mathematicae Mathematics-Applied Mathematics

CiteScore

0.30

自引率

0.00%

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