Regularized solution for backward heat equation in Sobolev space
Sujeewa Hapuarachchi, Yongzhi S. Xu
Source abstract
Inverse problems in partial deferential equations are severely ill posed in the sense of Hadamard. So the heat equation with a terminal condition problem is ill posed even in the sobolev space so regularization is needed. In this paper, we discuss about the convergence result of the approximation problem in the Sobolev space , which is well posed. By using a small parameter, we construct an approximation problem and use a quasi‐boundary value method to regularize nonlinear heat equation. Finally, we prove the approximation solution converges to the original solution whenever the parameter goes to zero in .
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