Nonlinear Wavelet Methods for High-dimensional Backward Heat Equation

来源：Acta Mathematica Sinica-English Series, 2013, 29(5): 913-922.

DOI：10.1007/s10114-013-1136-1

• Backward heat equation
• nonlinear wavelet method
• convergence

The backward heat equation is a typical ill-posed problem. In this paper, we shall apply a dual least squares method connecting Shannon wavelet to the following equation
{u(t)(x,y,t) = u(xx)(x,y,t) + u(yy)(x,y,t), x is an element of R, y is an element of R, 0 <= t < 1,
u(x,y,1) = phi(x,y), x is an element of R, y is an element of R.
Motivated by Reginska's work, we shall give two nonlinear approximate methods to regularize the approximate solutions for high-dimensional backward heat equation, and prove that our methods are convergent.

• 出版日期2013-5
• 单位北京工业大学