Inverse parabolic problems

Abstract

In this chapter we consider the second-order parabolic equation

$$ {a_0}{\partial _t}u - div(a\nabla u) + b\nabla u + cu = f{\mkern 1mu} in{\mkern 1mu} Q = \Omega \times (0,{\mkern 1mu} T), $$

(9.0.1)

where Ω is a bounded domain the space ℝⁿ with the C ²-smooth boundary ∂Ω. In Section 9.5 we study the nonlinear equation

$$ {a_0}(x,u){u_t} - \Delta u + c(x,{\mkern 1mu} t,{\mkern 1mu} u) = 0{\mkern 1mu} in{\mkern 1mu} Q. $$

(9.0.1n)