کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5774557 | 1413562 | 2017 | 31 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A variational approach to symmetry, monotonicity, and comparison for doubly-nonlinear equations
ترجمه فارسی عنوان
یک رویکرد تنوع برای تقارن، یکنواختی و مقایسه معادلات دوگانه غیر خطی
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
We advance a variational method to prove qualitative properties such as symmetries, monotonicity, upper and lower bounds, sign properties, and comparison principles for a large class of doubly-nonlinear evolutionary problems including gradient flows, some nonlocal problems, and systems of nonlinear parabolic equations. Our method is based on the so-called Weighted-Energy-Dissipation (WED) variational approach. This consists in defining a global parameter-dependent functional over entire trajectories and proving that its minimizers converge to solutions to the target problem as the parameter goes to zero. Qualitative properties and comparison principles can be easily proved for minimizers of the WED functional and, by passing to the limit, for the limiting problem. Several applications of the abstract results to systems of nonlinear PDEs and to fractional/nonlocal problems are presented. Eventually, we present some extensions of this approach in order to deal with rate-independent systems and hyperbolic problems.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 456, Issue 2, 15 December 2017, Pages 1303-1328
Journal: Journal of Mathematical Analysis and Applications - Volume 456, Issue 2, 15 December 2017, Pages 1303-1328
نویسندگان
Stefano Melchionna,