Regularization for a nonlinear backward parabolic problem with continuous spectrum operator

A regularization method for solving a nonlinear backward inverse heat conduction problem using discrete mollification method

The present essay scrutinizes the application of discrete mollification as a filtering procedure to solve a nonlinear backward inverse heat conduction problem in one dimensional space. These problems are seriously ill-posed. So, we combine discrete mollification and space marching method to address the ill-posedness of the proposed problem. Moreover, a proof of stability and<b...

A numerical scheme for solving nonlinear backward parabolic problems

‎In this paper a nonlinear backward parabolic problem in one‎ ‎dimensional space is considered‎. ‎Using a suitable iterative‎ ‎algorithm‎, ‎the problem is converted to a linear backward parabolic‎ ‎problem‎. ‎For the corresponding problem‎, ‎the backward finite‎ ‎differences method with suitable grid size is applied‎. ‎It is shown‎ ‎that if the coefficients satisfy some special conditions‎, ‎th...

A Regularization of the Backward Problem for Nonlinear Parabolic Equation with Time-Dependent Coefficient

a numerical scheme for solving nonlinear backward parabolic problems

‎in this paper a nonlinear backward parabolic problem in one‎ ‎dimensional space is considered‎. ‎using a suitable iterative‎ ‎algorithm‎, ‎the problem is converted to a linear backward parabolic‎ ‎problem‎. ‎for the corresponding problem‎, ‎the backward finite‎ ‎differences method with suitable grid size is applied‎. ‎it is shown‎ ‎that if the coefficients satisfy some special conditions‎, ‎th...

Regularization Method for Parabolic Equation with Variable Operator

Consider the initial boundary value problem for the equation ut =−L(t)u, u(1)= w on an interval [0,1] for t > 0, where w(x) is a given function in L2(Ω) and Ω is a bounded domain in Rn with a smooth boundary ∂Ω. L is the unbounded, nonnegative operator in L2(Ω) corresponding to a selfadjoint, elliptic boundary value problem in Ω with zero Dirichlet data on ∂Ω. The coefficients of L are assumed ...