A class of Hamilton-Jacobi equations with constraint: uniqueness and constructive approach
A class of Hamilton-Jacobi equations with constraint: uniqueness and constructive approach
复制标题
一类带约束的Hamilton-Jacobi方程：唯一性和构造性方法
DOI：
10.1016/j.jde.2015.11.027
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
J. Roquejoffre
中科院分区：
文献类型：
--
作者：
S. Mirrahimi;J. Roquejoffre
讨论了一类含时的Hamilton-Jacobi方程，其中时间的未知函数使解的最大值保持为常数0。我们的主要结果是，完整的问题有一个唯一的粘性解决方案，这实际上是经典的。其动机是一个选择-突变模型，在小扩散的限制下，该模型的Hamilton-Jacobi方程的解集中在零水平集上，通过注意到动态规划原理的结果，Hamilton-Jacobi方程的解是经典的，得到了唯一性.这样就可以写出一个求解的最大值的常微分方程，并把整个问题当作一个非标准柯西问题来处理。
We discuss a class of time-dependent Hamilton–Jacobi equations, where an unknown function of time is intended to keep the maximum of the solution to the constant value 0. Our main result is that the full problem has a unique viscosity solution, which is in fact classical. The motivation is a selection–mutation model which, in the limit of small diffusion, exhibits concentration on the zero level set of the solution of the Hamilton–Jacobi equation.Uniqueness is obtained by noticing that, as a consequence of the dynamic programming principle, the solution of the Hamilton–Jacobi equation is classical. It is then possible to write an ODE for the maximum of the solution, and treat the full problem as a nonstandard Cauchy problem.