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arXiv · 2202.11315

A nonlinear semigroup approach to Hamilton-Jacobi equations--revisited

Panrui Ni·Lin Wang
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Abstract

We consider the Hamilton-Jacobi equation \[{H}(x,Du)+\lambda(x)u=c,\quad x\in M, \] where $M$ is a connected, closed and smooth Riemannian manifold. The functions ${H}(x,p)$ and $\lambda(x)$ are continuous. ${H}(x,p)$ is convex, coercive with respect to $p$, and $\lambda(x)$ changes the signs. The first breakthrough to this model was achieved by Jin-Yan-Zhao \cite{JYZ} under the Tonelli conditions. In this paper, we consider more detailed structure of the viscosity solution set and large time behavior of the viscosity solution on the Cauchy problem.

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Panrui Ni, Lin Wang. 2022-02-23. A nonlinear semigroup approach to Hamilton-Jacobi equations--revisited. https://arxiv.org/abs/2202.11315

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