论文标题
汉密尔顿 - 雅各比方程的非线性半群方法 - 玩具模型
Nonlinear semigroup approach to Hamilton-Jacobi equations -- A toy model
论文作者
论文摘要
In this paper, we discuss the existence and multiplicity problem of viscosity solution to the Hamilton-Jacobi equation $$h(x,d_x u)+λ(x)u=c,\quad x\in M,$$ where $M$ is a closed manifold and $λ:M\rightarrow\mathbb{R}$ changes signs on $M$, via nonlinear semigroup method.事实证明，当参数$ c $超过临界值时，就会发生分叉现象。作为主要结果的应用，我们详细分析了一维示例的粘度解的结构。
In this paper, we discuss the existence and multiplicity problem of viscosity solution to the Hamilton-Jacobi equation $$h(x,d_x u)+λ(x)u=c,\quad x\in M,$$ where $M$ is a closed manifold and $λ:M\rightarrow\mathbb{R}$ changes signs on $M$, via nonlinear semigroup method. It turns out that a bifurcation phenomenon occurs when parameter $c$ strides over the critical value. As an application of the main result, we analyse the structure of the set of viscosity solutions of an one-dimensional example in detail.
