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

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