The mathematical properties of a nonlinear parabolic equation arising in the modelling of non-newtonian flows are investigated. The peculiarity of this equation is that it may degenerate into a hyperbolic equation (in fact a linear advection equation). Depending on the initial data, at least two situations can be encountered: the equation may have a unique solution in a convenient class, or it ...

The paper deals with a degenerate and singular parabolic equation with nonlinear boundary condition. We first get the behavior of the solution at infinity, and establish the critical global existence exponent and critical Fujita exponent for the fast diffusive equation, furthermore give the blow-up set and upper bound of the blow-up rate for the nonglobal solutions.

The coefficient inverse problem for the degenerate parabolic equation is investigated. minor of this polynomial first power with respect to space variable two unknown time-dependent functions. investigation carried out under given inhomogeneous initial condition, Dirichlet boundary conditions and integral overdetermination conditions. We establish unique solvability named case strong degenerati...