کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4620293 1339459 2009 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Stability results for the heat equation backward in time
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Stability results for the heat equation backward in time
چکیده انگلیسی

For the heat equation backward in timeut=uxx,x∈R,t∈(0,T),‖u(⋅,T)−φ(⋅)‖Lp(R)⩽ϵ subject to the constraint‖u(⋅,0)‖Lp(R)⩽E‖u(⋅,0)‖Lp(R)⩽E with T>0T>0, φ∈Lp(R)φ∈Lp(R), 0<ϵ0c>0 such that‖u1(⋅,t)−u2(⋅,t)‖Lp(R)⩽cϵt/TE1−t/T,∀t∈[0,T]. In case p=2p=2 we establish stability estimates of Hölder type for all derivatives with respect to x and t   of the solutions. We suggest a useful strategy of choosing mollification parameters which provides a continuity at t=0t=0 when an additional condition on the smoothness of u(x,0)u(x,0) is given. Furthermore, we propose a stable marching difference scheme for this ill-posed problem and test several related numerical methods for it.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 353, Issue 2, 15 May 2009, Pages 627–641
نویسندگان
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