## On the uniqueness and stability of BV solutions for nonlinear diffusion equations.(English)Zbl 0726.35063

Uniqueness and stability results for BV solutions of the Cauchy problem for a nonlinear diffusion equation of the form $u_ t=\Delta A(u)+\nabla B(u),\quad u(0,x)=u_ 0(x)$ are proved under the general assumption that A(s) is strictly increasing.
Reviewer: S.Tersian (Russe)

### MSC:

 35K57 Reaction-diffusion equations 35B35 Stability in context of PDEs

### Keywords:

Uniqueness; stability; BV solutions; Cauchy problem