A quasi-linear evolution equation and the method of Galerkin

Author:
R. W. Dickey

Journal:
Proc. Amer. Math. Soc. **37** (1973), 149-156

MSC:
Primary 35Q99

MathSciNet review:
0308620

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Abstract: In this paper it is shown that under specified conditions on the initial data a certain infinite coupled system of ordinary differential equations has a solution satisfying an auxiliary convergence condition. The infinite system discussed is essentially the Galerkin expansion of the solution to a given quasi-linear wave equation. The results obtained suffice to prove the existence of a solution to this wave equation.

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DOI:
https://doi.org/10.1090/S0002-9939-1973-0308620-3

Article copyright:
© Copyright 1973
American Mathematical Society