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Local existence for solutions of fully non-linear wave equations

✍ Scribed by Peter Lesky Jr

Publisher
John Wiley and Sons
Year
1991
Tongue
English
Weight
1014 KB
Volume
14
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

Let Ξ© be a domain in ℝ^n^ and let __m__Ο΅ β„•; be given. We study the initial‐boundary value problem for the equation
with a homogeneous Dirichlet boundary condition; here u is a scalar function, \documentclass{article}\pagestyle{empty}\begin{document}$ \bar D_x^m u: = (\partial _x^\alpha u)_{|\alpha | \le m} $\end{document} and certain restrictions are made on F guaranteeing that energy estimates are possible. We prove the existence of a value of T>0 such that a unique classical solution u exists on [0, T]Γ—Ξ©. Furthermore, we show that T β†’ ∞ if the data tend to zero.

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