Title :
Regularized Wavelet Solutions for Ill-posed Nonhomogeneous Parabolic Equations
Author :
Wang, Jin-ru ; Zhou, Yuan
Author_Institution :
Dept. of Appl. Math., Beijing Univ. of Technol., Beijing, China
Abstract :
We consider the nonhomogeneous problem uxx(x, t) = ut(x, t) + f(x, t), 0 ≤ x <; 1, t ≥ 0, where the Cauchy data g(t) is given at x = 1. This is an ill-posed problem in the sense that a small disturbance on the boundary g(t) can produce a big alteration on its solution (if it exists). In this paper, we shall define a Meyer wavelet solution to obtain well-posed solution in the scaling space Vj. We shall also show that under certain conditions this regularized solution is convergent to the exact solution. In the previous papers, most of the theoretical results concerning the error estimate are about the homogeneous equation, i.e., f(x, t) ≡ 0.
Keywords :
initial value problems; parabolic equations; Cauchy data; Meyer wavelet solution; error estimate; ill-posed nonhomogeneous parabolic equations; nonhomogeneous problem; regularized wavelet solutions; scaling space; well-posed solution; Equations; Fourier transforms; Heating; Multiresolution analysis; Vectors; Wavelet transforms; Ill-posed problem; Parabolic equation; Regularized solution; Wavelet;
Conference_Titel :
Chaos-Fractals Theories and Applications (IWCFTA), 2012 Fifth International Workshop on
Conference_Location :
Dalian
Print_ISBN :
978-1-4673-2825-8
DOI :
10.1109/IWCFTA.2012.12