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Uniqueness of the Rothe method for the Burgers equation with piecewise continuous initial data. (English) Zbl 0713.65061
Differential equations and their applications, Proc. 7th Conf., Equadiff 7, Prague/Czech. 1989, Teubner-Texte Math. 118, 281-284 (1990).
[For the entire collection see Zbl 0704.00019.]
The Rothe method is applied to the Cauchy problem of Burgers’ equation with the corresponding entropy condition. The question of uniqueness is treated without any restriction if the initial data are piecewise continuous and compactifiable at the infinity. The important role of the entropy condition is discussed.
Reviewer: L.G.Vulkov
MSC:
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)