In this paper,a Cauchy problem of two-dimensional heat conduction equation is investigated.This is a severely iⅡ-posed problem.Based on the solution of Cauchy problem of two-dimensional heat conduction equation,we pr...In this paper,a Cauchy problem of two-dimensional heat conduction equation is investigated.This is a severely iⅡ-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.展开更多
基金supported by the National Natural Science Foundation of China(11101109,11271102)and the Natural Science Foundation of Heilongjiang Province of China(A201107).
文摘In this paper,a Cauchy problem of two-dimensional heat conduction equation is investigated.This is a severely iⅡ-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.