In this paper, a Cauchy problem of two-dimensional heat conduction
equation is investigated. This is a severely ill-posed problem.
Based on the solution of Cauchy problem of two-dimensional heat
conduction equation, we propose to solve this problem by modifying
the kernel, which generates a well-posed problem. Error estimates
between the exact solution and the regularized solution are given.
We provide a numerical experiment to illustrate the main results.