کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1708688 1012829 2012 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A source identification problem related to mathematical model of laser surface heating
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مکانیک محاسباتی
پیش نمایش صفحه اول مقاله
A source identification problem related to mathematical model of laser surface heating
چکیده انگلیسی

A mathematical model of two-dimensional laser surface heating for the hardening of metallic materials is proposed. The model is governed by the heat equation ut−Δu=m(t)δγ(x−ω(t))ut−Δu=m(t)δγ(x−ω(t)), (x,t)∈Ω(x,t)∈Ω, with the pointwise source term δγ(y)δγ(y), satisfying the initial u(x,0)=g(x)u(x,0)=g(x) and boundary u(x,t)=0u(x,t)=0, x∈∂Ωx∈∂Ω, conditions. The pair of source terms 〈m(t),ω(t)〉〈m(t),ω(t)〉 is assumed to be unknown. The two-valued (m(t)=0m(t)=0 or m(t)=m0>0m(t)=m0>0) function m(t)m(t) is treated as the intensity of the laser beam, and the function ω(t)ω(t) describes the laser beam trajectory. The identification problem consists of determining the pair of source terms 〈m(t),ω(t)〉〈m(t),ω(t)〉 such that the corresponding heat function u(x,t)u(x,t) satisfies the condition ‖u−v‖L2(Ω)≤ε‖u−v‖L2(Ω)≤ε, where the smooth function v(x,t)v(x,t) is assumed to be known (experimentally), and ε>0ε>0 is a given-in-advance parameter. Besides the existence result, the structure of the optimal trajectory is also described.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics Letters - Volume 25, Issue 10, October 2012, Pages 1480–1485
نویسندگان
, , ,