## Sur l’équation générale $$u_ t=\phi (u)_{xx}-\psi (u)_ x+v$$. (On the general equation $$u_ t=\phi (u)_{xx}-\psi (u)_ x+v)$$.(French)Zbl 0586.35016

We study the equation $$u_ t=\phi (u)_{xx}-\psi (u)_ x+v$$ assuming only that $$\phi$$ and $$\psi$$ are continuous functions of $${\mathbb{R}}$$ into $${\mathbb{R}}$$ with $$\phi$$ non decreasing. In particular we show the continuous dependence of ”mild solution” with respect to $$\phi$$, $$\psi$$, v, $$u_ 0$$.

### MSC:

 35G20 Nonlinear higher-order PDEs 47H20 Semigroups of nonlinear operators 35D05 Existence of generalized solutions of PDE (MSC2000) 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs