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Local existence for solutions of fully non-linear wave equations
Authors:Peter Lesky
Abstract:Let Ω be a domain in ?n and let m? ?; be given. We study the initial-boundary value problem for the equation equation image with a homogeneous Dirichlet boundary condition; here u is a scalar function, $ \bar D_x^m u: = (\partial _x^\alpha u)_{|\alpha | \le m} $equation image 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]×Ω. Furthermore, we show that T → ∞ if the data tend to zero.
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