کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8899104 | 1631508 | 2018 | 34 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Fractional partial differential equations with boundary conditions
ترجمه فارسی عنوان
معادلات دیفرانسیل جزئی مضاعف با شرایط مرزی
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for modelling using spatial fractional derivatives. We show well-posedness of the associated Cauchy problems in C0(Ω) and L1(Ω). In order to do so we develop a new method of embedding finite state Markov processes into Feller processes on bounded domains and then show convergence of the respective Feller processes. This also gives a numerical approximation of the solution. The proof of well-posedness closes a gap in many numerical algorithm articles approximating solutions to fractional differential equations that use the Lax-Richtmyer Equivalence Theorem to prove convergence without checking well-posedness.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 264, Issue 2, 15 January 2018, Pages 1377-1410
Journal: Journal of Differential Equations - Volume 264, Issue 2, 15 January 2018, Pages 1377-1410
نویسندگان
Boris Baeumer, Mihály Kovács, Harish Sankaranarayanan,