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	Volume 3, Issue 2 Pg 87 - 172 (June 2010)
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International Journal of Numerical Methods and Applications

where the Cauchy data

is given at

This is an ill-posed problem in the sense that a small disturbance on the boundary

can produce a big alteration in its solution (if it exists). In this paper, we define a Meyer wavelet solution to obtain the well-posed solution in the scaling space

We 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 were about the homogeneous equation, i.e.,

International Journal of Numerical Methods and Applications
Volume 3, Issue 2, Pages 133 - 150 (June 2010)

REGULARIZED SOLUTION FOR THE NONHOMOGENEOUS PARABOLIC EQUATION USING MEYER WAVELETS
Jin-Ru Wang

Abstract:
We consider the nonhomogeneous problem

where the Cauchy data

is given at

This is an ill-posed problem in the sense that a small disturbance on the boundary

can produce a big alteration in its solution (if it exists). In this paper, we define a Meyer wavelet solution to obtain the well-posed solution in the scaling space

Keywords and phrases: nonhomogeneous parabolic equation, ill-posed problems, multi-resolution analysis, Meyer wavelet.

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