Simultaneous reconstruction of the source term and the surface heat transfer coefficient

We study the problem of identifying unknown source terms in an inverse parabolic problem, when the overspecified (measured) data are given in form of Dirichlet boundary condition u(0,t)=h(t) and u(x,t)=q(x,t),(x,t, is an element of Omega(t1)degrees, where Omega(t1)degrees is an arbitrarily prescribed subregion. The main goal here is to show that the gradient of cost functional can be expressed via the solutions of the direct and corresponding adjoint problems. We prove Holder continuity of the cost functional and derive the Lipschitz constant in the explicit form via the given data. On the basis of the obtained results, we propose a monotone iteration process. Copyright (c) 2014 John Wiley & Sons, Ltd.