Some problems of the qualitative theory of nonlinear degenerate second- order parabolic equations.

*(English)*Zbl 0642.35047A survey on modern theory of degenerate parabolic equations of the form ${u}_{t}=F(x,t,u,{u}_{x},{u}_{xx})\xb7$

Investigations on such equations are important, because the equation of non-Newtonian filtration, the equation of rapid diffusion, the equations of nonlinear heat conduction and some other ones contain degeneracies.

The principal objects of investigation are generalized solutions. Chapter 1 is discussing problems of their existence and uniqueness. Estimates and regularity problems are considered in chapter 2. Short time and long time behavior of solutions is described in chapters 3 and 4. A list of about 300 references is presented.

Reviewer: I.Dorfman

##### MSC:

35K65 | Parabolic equations of degenerate type |

35K15 | Second order parabolic equations, initial value problems |

35D05 | Existence of generalized solutions of PDE (MSC2000) |

35B40 | Asymptotic behavior of solutions of PDE |

35K60 | Nonlinear initial value problems for linear parabolic equations |