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Comparison of solutions of Hamilton-Jacobi equations with different initial conditions
Consider a Hamilton-Jacobi equation:
$$u_{t} + f(u_{x}) = 0 \quad (x,t) \in \mathbb{R}\times [0,+\infty)$$
with two possible initial conditions $u(x,0) = g_{i}(x)$ for $x \in \mathbb{R}$ and $i=1,2$. ...
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