کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8899002 1631506 2018 39 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Loss of boundary conditions for fully nonlinear parabolic equations with superquadratic gradient terms
ترجمه فارسی عنوان
از دست دادن شرایط مرزی برای معادلات پارابولی کاملا غیر خطی با شرایط گرادیان سوپرکراداشت
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی
We study whether the solutions of a fully nonlinear, uniformly parabolic equation with superquadratic growth in the gradient satisfy initial and homogeneous boundary conditions in the classical sense, a problem we refer to as the classical Dirichlet problem. Our main results are: the nonexistence of global-in-time solutions of this problem, depending on a specific largeness condition on the initial data, and the existence of local-in-time solutions for initial data C1 up to the boundary. Global existence is know when boundary conditions are understood in the viscosity sense, what is known as the generalized Dirichlet problem. Therefore, our result implies loss of boundary conditions in finite time. Specifically, a solution satisfying homogeneous boundary conditions in the viscosity sense eventually becomes strictly positive at some point of the boundary.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 264, Issue 4, 15 February 2018, Pages 2897-2935
نویسندگان
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