This paper deals with the inverse time problem for an axisymmetric heat equation. The problem is ill-posed. A modified Tikhonov regularization method is applied to formulate regularized solution which is stably conver...This paper deals with the inverse time problem for an axisymmetric heat equation. The problem is ill-posed. A modified Tikhonov regularization method is applied to formulate regularized solution which is stably convergent to the exact one. estimate between the approximate solution and exact technical inequality and improving a priori smoothness Meanwhile, a logarithmic-HSlder type error solution is obtained by introducing a rather assumption.展开更多
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 Motivated by Reginska＇s work, we shall give ...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 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.展开更多
Abstract The authors establish the null controllability for some systems coupled by two backward stochastic heat equations. The desired controllability result is obtained by means of proving a suitable observability e...Abstract The authors establish the null controllability for some systems coupled by two backward stochastic heat equations. The desired controllability result is obtained by means of proving a suitable observability estimate for the dual system of the controlled system.展开更多
The regularization of ill-posed problems has become a useful tool in studying initial value problems that do not adhere to certain desired properties such as continuous dependence of solutions on initial data.Because ...The regularization of ill-posed problems has become a useful tool in studying initial value problems that do not adhere to certain desired properties such as continuous dependence of solutions on initial data.Because direct computation of the solution becomes difficult in this situation,many authors have alternatively approximated the solution by the solution of a closely defined well posed problem.In this paper,we demonstrate this process of regularization for nonautonomous ill-posed problems including the backward heat equation with a time-dependent diffusion coefficient.In the process,we provide two different approximate well posed models and numerically compare convergence rates of their solutions to a known solution of the original ill-posed problem.展开更多
基金Supported by National Natural Science Foundation of China (Grant No.10671085)Fundamental Research Fund for Natural Science of Education Department of He'nan Province of China (Grant No.2009Bl10007)Hight-level Personnel fund of He'nan University of Technology (Grant No.2007BS028)
文摘This paper deals with the inverse time problem for an axisymmetric heat equation. The problem is ill-posed. A modified Tikhonov regularization method is applied to formulate regularized solution which is stably convergent to the exact one. estimate between the approximate solution and exact technical inequality and improving a priori smoothness Meanwhile, a logarithmic-HSlder type error solution is obtained by introducing a rather assumption.
基金Supported by Beijing Natural Science Foundation(Grant No.1092003)Beijing Educational Committee Foundation(Grant No.PHR201008022) National Natural Science Foundation of China(Grant No.11271038)1)Corresponding author
文摘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 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.
基金Project supported by the National Natural Science Foundation of China(No.11101070)the Grant MTM2011-29306-C02-00 of the MICINN,Spain+4 种基金the Project PI2010-04 of the Basque Governmentthe ERC Advanced Grant FP7-246775 NUMERIWAVESthe ESF Research Networking Programme OPT-PDEScientific Research Fund of Sichuan Provincial Education Department of China(No.10ZC110) the project Z1062 of Leshan Normal University of China
文摘Abstract The authors establish the null controllability for some systems coupled by two backward stochastic heat equations. The desired controllability result is obtained by means of proving a suitable observability estimate for the dual system of the controlled system.
文摘The regularization of ill-posed problems has become a useful tool in studying initial value problems that do not adhere to certain desired properties such as continuous dependence of solutions on initial data.Because direct computation of the solution becomes difficult in this situation,many authors have alternatively approximated the solution by the solution of a closely defined well posed problem.In this paper,we demonstrate this process of regularization for nonautonomous ill-posed problems including the backward heat equation with a time-dependent diffusion coefficient.In the process,we provide two different approximate well posed models and numerically compare convergence rates of their solutions to a known solution of the original ill-posed problem.
