We consider the parabolic equation with variable coefficients k（x）Uxx = ut, 0,x ≤1, t≥ 0, where 0 〈 α ≤ k（x） 〈 ＋∞, the solution on the boundary x = 0 is a given function g and ux（0,t） = 0. We use wavelet...We consider the parabolic equation with variable coefficients k（x）Uxx = ut, 0,x ≤1, t≥ 0, where 0 〈 α ≤ k（x） 〈 ＋∞, the solution on the boundary x = 0 is a given function g and ux（0,t） = 0. We use wavelet Galerkin method with Meyer multi-resolution analysis to obtain a wavelet approximating solution, and also get an estimate between the exact solution and the wavelet approximating solution of the problem.展开更多
We consider the problem K（x）Uxx = utt , 0 〈 x 〈 1, t 〉 0, with the boundary condition u（O,t） = g（t） E LZ（R） and ux（O,t） = 0, where K（x） is continuous and 0 〈α≤ K （x） 〈 ＋∞. This is an ill-posed p...We consider the problem K（x）Uxx = utt , 0 〈 x 〈 1, t 〉 0, with the boundary condition u（O,t） = g（t） E LZ（R） and ux（O,t） = 0, where K（x） is continuous and 0 〈α≤ K （x） 〈 ＋∞. This is an ill-posed problem in the sense that, if the solution exists, it does not depend continuously on g. Considering the existence of a solution u（x, .） E H2（R） and using a wavelet Galerkin method with Meyer multiresolution analysis, we regularize the ill-posedness of the problem. Furthermore we prove the uniqueness of the solution for this problem.展开更多
基金Supported by the National Nature Science Foundation (No.10871012)the Beijing Nature Science Foundation(No.1082003)the Doctoral foundation of Beijing University of Technology (No.52006011200702)
文摘We consider the parabolic equation with variable coefficients k（x）Uxx = ut, 0,x ≤1, t≥ 0, where 0 〈 α ≤ k（x） 〈 ＋∞, the solution on the boundary x = 0 is a given function g and ux（0,t） = 0. We use wavelet Galerkin method with Meyer multi-resolution analysis to obtain a wavelet approximating solution, and also get an estimate between the exact solution and the wavelet approximating solution of the problem.
文摘We consider the problem K（x）Uxx = utt , 0 〈 x 〈 1, t 〉 0, with the boundary condition u（O,t） = g（t） E LZ（R） and ux（O,t） = 0, where K（x） is continuous and 0 〈α≤ K （x） 〈 ＋∞. This is an ill-posed problem in the sense that, if the solution exists, it does not depend continuously on g. Considering the existence of a solution u（x, .） E H2（R） and using a wavelet Galerkin method with Meyer multiresolution analysis, we regularize the ill-posedness of the problem. Furthermore we prove the uniqueness of the solution for this problem.
