A quasi-reversibility method for solving nonhomogeneous sideways heat equation

Abstract

We consider solving a severely ill-posed problem for determining the surface temperature and heat flux distribution of the nonhomogeneous sideways heat equation by a quasi-reversibility regularization method. An analytical solution is deduced based on the Fourier transform, and then, the logarithmic-type error estimate for the regularized solution is achieved. Finally, three numerical examples, including smooth and non-smooth functions, validate the feasibility and effectiveness of the proposed approach.

Keywords

• ill-posed problem
• nonhomogeneous sideways heat equation
• a quasi-reversibility method
• error estimate
• 35r25
• 35r30
• 65j20
• 65m30