On the numerical solution of higher order nonlinear parabolic equations

Summary

This paper deals with the numerical approximation of weak solutions of the first initial, boundary value problem for the higher order, nonlinear parabolic equation

$$\sum\limits_{|\alpha | , |\beta | \leqq p} {D^\alpha (a_{\alpha \beta } (x,t)) \leqq D^\beta u - \partial u/\partial t = f} $$

wheref=f(x, t, D ^v u), |v|≤p−1, p≥1 is an integer and α, β,v are multi-indices.

Zusammenfassung

Diese Arbeit behandelt die numerische Approximation von schwachen Lösungen der ersten Anfangs-Randwertaufgabe für die nichtlineare parabolische Gleichung höherer Ordnung

$$\sum\limits_{|\alpha | , |\beta | \leqq p} {D^\alpha (a_{\alpha \beta } (x,t)) \leqq D^\beta u - \partial u/\partial t = f} $$

wof=f(x, t, D ^v u), |v|≤p−1, p≥1 ganz, und wo α, β,v multi-Indices sind.