regularization method for parabolic equation with variable operator

طريقة التنظيم لمعادلة مكافئة ذات مؤثر متغير

Clicks: 120
ID: 241111
2005
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Abstract
Consider the initial boundary value problem for the equation ut=−L(t)u, u(1)=w on an interval [0,1] for t>0, where w(x) is a given function in L2(Ω) and Ω is a bounded domain in ℝn with a smooth boundary ∂Ω. L is the unbounded, nonnegative operator in L2(Ω) corresponding to a selfadjoint, elliptic boundary value problem in Ω with zero Dirichlet data on ∂Ω. The coefficients of L are assumed to be smooth and dependent of time. It is well known that this problem is ill-posed in the sense that the solution does not depend continuously on the data. We impose a bound on the solution at t=0 and at the same time allow for some imprecision in the data. Thus we are led to the constrained problem. There is built an approximation solution, found error estimate for the applied method, given preliminary error estimates for the approximate method.
نعتبر مسألة القيمة الابتدائية والحدية للمعادلة $u_t = -L(t)u$، و$u(1) = w$ على الفترة $[0,1]$ لـ $t > 0$، حيث $w(x)$ دالة معطاة في $L^2(\Omega)$، و$\Omega$ نطاق محدود في $\mathbb{R}^n$ ذو حدود ملساء $\partial\Omega$. ويمثل $L$ مؤثراً غير محدود وغير سالب في $L^2(\Omega)$ يناظر مسألة قيمة حدية إهليلجية ومترافقة ذاتياً في $\Omega$ مع شروط ديريكليه صفرية على $\partial\Omega$. يُفترض أن معاملات $L$ ملساء وتعتمد على الزمن. ومن المعروف جيداً أن هذه المسألة سيئة الوضع، بمعنى أن الحل لا يعتمد بشكل مستمر على المعطيات. نفرض حداً على الحل عند $t = 0$، ونسمح في الوقت ذاته بوجود بعض عدم الدقة في المعطيات. وبذلك نصل إلى المسألة المقيدة. تم بناء حل تقريبي، وإيجاد تقدير للخطأ بالنسبة للطريقة المطبقة، وتقديم تقديرات أولية للخطأ للطريقة التقريبية.
Reference Key
burmistrova2005journalregularization Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Valentina Burmistrova
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Journal Chemico-biological interactions
Year 2005
DOI
10.1155/JAM.2005.383
URL
http://dx.doi.org/10.1155/JAM.2005.383
Keywords
mathematics

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