A Modified Kernel Method for Solving Cauchy Problem of Two-Dimensional Heat Conduction Equation (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, a Cauchy problem of two-dimensional heat conductionequation is investigated. This is a severely ill-posed problem.Based on the solution of Cauchy problem of two-dimensional heatconduction equation, we propose to solve this problem by modifyingthe kernel, which generates a well-posed problem. Error estimatesbetween the exact solution and the regularized solution are given.We provide a numerical experiment to illustrate the main results.