An inverse problem for a linearized model in the theory of combustion.

In the recent paper [Colombo, Physica D 236: 81–89, 2007] the author investigates an inverse problem arising in the theory of combustion. The problem studied is: determine the temperature u and the convolution memory kernel k in the evolution equation given suitable initial-boundary conditions and the following additional restriction on u: ∫Ω φ( x) u( t, x) dx = g( t), where φ and g are given functions. The main results are a local in time existence theorem and a global in time uniqueness result. In this paper we complete the study considering the linearized version of the model. We prove that, if F( u( t, x), ∇ u( t, x)) is sublinear, then the inverse problem has a unique global in time solution. [ABSTRACT FROM AUTHOR]