On the Uniqueness for One-Dimensional Constrained Hamilton-Jacobi Equations.
2018
The goal of this paper is to study uniqueness of a one-dimensional Hamilton-Jacobi equation \begin{equation*}
\begin{cases}
u_t=|u_x|^2+R(x,I(t)) &\text{in }\mathbb{R} \times (0,\infty),
\max_{\mathbb{R}} u(\cdot,t)=0 &\text{on }[0,\infty),
\end{cases} \end{equation*} with an initial condition $u_0(x,0)=u_0(x)$ on $\mathbb{R}$. A reaction term $R(x,I(t))$ is given while $I(t)$ is an unknown constraint (Lagrange multiplier) that forces maximum of $u$ to be always zero. In the paper, we prove uniqueness of a pair of unknowns (u,I) using dynamic programming principle in one dimensional space for some particular class of nonseparable reaction $R(x,I(t))$.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
11
References
2
Citations
NaN
KQI