Convergence & rates for Hamilton–Jacobi equations with Kirchoff junction conditions
Tóm tắt
We investigate rates of convergence for two approximation schemes of time-independent and time-dependent Hamilton–Jacobi equations with Kirchoff junction conditions. We analyze the vanishing viscosity limit and monotone finite-difference schemes. Following recent work of Lions and Souganidis, we impose no convexity assumptions on the Hamiltonians. For stationary Hamilton–Jacobi equations, we obtain the classical $$\epsilon ^{\frac{1}{2}}$$ rate, while we obtain an $$\epsilon ^{\frac{1}{7}}$$ rate for approximations of the Cauchy problem. In addition, we present a number of new techniques of independent interest, including a quantified comparison proof for the Cauchy problem and an equivalent definition of the Kirchoff junction condition.
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