کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6425330 | 1633798 | 2016 | 24 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Maximal dissipation in Hunter-Saxton equation for bounded energy initial data
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Maximal dissipation in Hunter-Saxton equation for bounded energy initial data Maximal dissipation in Hunter-Saxton equation for bounded energy initial data](/preview/png/6425330.png)
چکیده انگلیسی
In [13] it was conjectured by Zhang and Zheng that dissipative solutions of the Hunter-Saxton equation, which are known to be unique in the class of weak solutions, dissipate the energy at the highest possible rate. The conjecture of Zhang and Zheng was proven in [4] by Dafermos for monotone increasing initial data with bounded energy. In this note we prove the conjecture in [13] in full generality. To this end we examine the evolution of the energy of any weak solution of the Hunter-Saxton equation. Our proof shows in fact that for every time t>0 the energy of the dissipative solution is not greater than the energy of any weak solution with the same initial data.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 290, 26 February 2016, Pages 590-613
Journal: Advances in Mathematics - Volume 290, 26 February 2016, Pages 590-613
نویسندگان
Tomasz CieÅlak, Grzegorz Jamróz,