On a class of fully nonlinear parabolic equations

We study the homogeneous Dirichlet problem for the fully nonlinear equation with the parameters , and . At the points where , the equation degenerates if , or becomes singular if . We derive conditions of existence and uniqueness of strong solutions, and study the asymptotic behavior of strong solutions as . Sufficient conditions for exponential or power decay of are derived. It is proved that for certain ranges of the exponents and σ, every strong solution vanishes in a finite time.