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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
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