A nonlinear semigroup approach to Hamilton-Jacobi equations–revisited
Abstract We consider the Hamilton-Jacobi equation H (x, D u)+ λ (x) u= c, x∈ M, where M is
a connected, closed and smooth Riemannian manifold. The functions H (x, p) and λ (x) are
continuous. H (x, p) is convex, coercive with respect to p, and λ (x) changes the signs. The
first breakthrough to this model was achieved by Jin-Yan-Zhao [11] 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. To the best of our …
a connected, closed and smooth Riemannian manifold. The functions H (x, p) and λ (x) are
continuous. H (x, p) is convex, coercive with respect to p, and λ (x) changes the signs. The
first breakthrough to this model was achieved by Jin-Yan-Zhao [11] 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. To the best of our …
Abstract
Abstract We consider the Hamilton-Jacobi equation H (x, D u)+ λ (x) u= c, x∈ M, where M is a connected, closed and smooth Riemannian manifold. The functions H (x, p) and λ (x) are continuous. H (x, p) is convex, coercive with respect to p, and λ (x) changes the signs. The first breakthrough to this model was achieved by Jin-Yan-Zhao [11] 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. To the best of our knowledge, it is the first detailed description of the large time behavior of the HJ equations with non-monotone dependence on the unknown function.
Elsevier
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