Abstract
We study the initial boundary value problem for the nonlinear wave equation:
wheren=4,5,u0,u1 are real valued functions and ∈0 is a sufficiently small positive constant. In this paper we shall show small solutions to (*) exist globally in time under the condition that the nonlinear termF:ℝ2→ℝ is quadratic with respect to ∂ t u and ∂ 2 t u.
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Hayashi, N. Global existence of small radially symmetric solutions to quadratic nonlinear wave equations in an exterior domain. Manuscripta Math 81, 15–39 (1993). https://doi.org/10.1007/BF02567842
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DOI: https://doi.org/10.1007/BF02567842