Maximum Principle for Nonlinear Parabolic Equations

Аннотация

A maximum principle is obtained for solutions of parabolic equations of the form

\( \mathcal{L}u-{u}_t=f\left(x,t,u, Du\right), \)

where

\( \mathcal{L}u=\sum \limits_{i,j}^n{a}_{ij}\left(x,t,u\right)\frac{\partial^2u}{\partial {x}_i\partial {x}_j}+\sum \limits_{i=1}^n{b}_i\left(x,t,u\right)\frac{\partial u}{\partial {x}_i}. \)