Finite time blow up of solutions to an inverse problem for a quasilinear parabolic equation with power nonlinearity

Abstract

We consider an inverse problem for quasilinear parabolic equations with type power nonlinearity. Sufficient conditions on initial data for blow up result are obtained with positive initial energy. Overdetermination condition is given as an integral form. To get the blow up result for considered nonlinear inverse parabolic equation, we use the concavity of a special positive function. The life span of the solution is also computed.