Existence results for inverse problems associated with a nonlinear parabolic equation

This paper deals with the determination of a pair (p,u) in the nonlinear parabolic equation ut − Δu + p(x)f (u) = 0, with initial and boundary conditions u(x, 0) = 0, u|∂Ω×[0,T ] = g, from the overspecified data u(. , T ) = q. The problem is reduced to a nonlinear operator equation and solved by taking advantage of a fixed point theory in ordered Banach spaces. Similarly, another form of overspecified data is considered.  2002 Elsevier Science (USA). All rights reserved