An Inverse Problem for Porous Medium Equation

An inverse problem for a nonlinear degenerate diffusion equation is considered. We look for unknown coefficient a(u) of the equation u _t = (a(u(u _x ) _x with zero initial values and nonmonotone impulse-like Dirichlet boundary condition. Measurements in an interior point x ₀ are taken as overposed data. An optimization approach is used. The case of the more general equation c(u)u _t = (a(u)u _x ) _x + b(u)u _x + s(u) is also considered.