کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4609718 1338524 2016 22 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A class of Hamilton–Jacobi equations with constraint: Uniqueness and constructive approach
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
A class of Hamilton–Jacobi equations with constraint: Uniqueness and constructive approach
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 260, Issue 5, 5 March 2016, Pages 4717–4738
نویسندگان
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