کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5774004 | 1413539 | 2017 | 37 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Generalized solutions in PDEs and the Burgers' equation
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In many situations, the notion of function is not sufficient and it needs to be extended. A classical way to do this is to introduce the notion of weak solution; another approach is to use generalized functions. Ultrafunctions are a particular class of generalized functions that has been previously introduced and used to define generalized solutions of stationary problems in [4,7,9,11,12]. In this paper we generalize this notion in order to study also evolution problems. In particular, we introduce the notion of Generalized Ultrafunction Solution (GUS) for a large family of PDEs, and we confront it with classical strong and weak solutions. Moreover, we prove an existence and uniqueness result of GUS's for a large family of PDEs, including the nonlinear Schroedinger equation and the nonlinear wave equation. Finally, we study in detail GUS's of Burgers' equation, proving that (in a precise sense) the GUS's of this equation provide a description of the phenomenon at microscopic level.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 263, Issue 10, 15 November 2017, Pages 6916-6952
Journal: Journal of Differential Equations - Volume 263, Issue 10, 15 November 2017, Pages 6916-6952
نویسندگان
Vieri Benci, Lorenzo Luperi Baglini,