Uniform Convergence of Wavelet Solution to the Sideways Heat Equation
English Series · 2010
We consider the problem uxx(x,t )= ut(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). We shall define a wavelet solution to obtain the well-posed approximating problem in the scaling space Vj. In the previous papers, the theoretical results concerning the error estimate are L 2 -norm and the solutions aren't stable at x =0 . However, in practice, the solution is usually required to be stable at the boundary. In this paper we shall give uniform convergence on interval x ∈ (0,1).