Hölder-type approximation for the spatial source term of a backward heat equation

TY - JOUR

T1 - Hölder-type approximation for the spatial source term of a backward heat equation

AU - Dang, Duc Trong

AU - Mach, Minh Nguyet

AU - Pham, Ngoc Dinh Alain

AU - Phan, Thanh Nam

PY - 2010/12

Y1 - 2010/12

N2 - We consider the problem of determining a pair of functions (u, f) satisfying the two-dimensional backward heat equation [image omitted] with a homogeneous Cauchy boundary condition, where and g are given approximately. The problem is severely ill-posed. Using an interpolation method and the truncated Fourier series, we construct a regularized solution for the source term f and provide Holder-type error estimates in both L2 and H1 norms. Numerical experiments are provided.

AB - We consider the problem of determining a pair of functions (u, f) satisfying the two-dimensional backward heat equation [image omitted] with a homogeneous Cauchy boundary condition, where and g are given approximately. The problem is severely ill-posed. Using an interpolation method and the truncated Fourier series, we construct a regularized solution for the source term f and provide Holder-type error estimates in both L2 and H1 norms. Numerical experiments are provided.

U2 - 10.1080/01630563.2010.528568

DO - 10.1080/01630563.2010.528568

M3 - Journal article

SN - 0163-0563

VL - 31

SP - 1386

EP - 1405

JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

IS - 12

ER -