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The global Cauchy problem for the critical non-linear wave equation in variable coefficients
Journal article

The global Cauchy problem for the critical non-linear wave equation in variable coefficients

S Ibrahim and M Majdoub
Comptes rendus de l'Académie des sciences. Série I. Mathématique, Vol.328(7), pp.579-584
01/04/1999
DOI: https://doi.org/10.1016/S0764-4442(99)80250-X

Abstract

Mathematics Physical Sciences Science & Technology
In this Note, we study the existence of global smooth solutions of the critical wave equation in variable coefficients in three dimensions of space: (E) square(A)u + \u\(4) u = partial derivative(t)(2)u - div (A(x) . del(x)u) + \u\(4)u = 0, R-t x R-x(3), where A is a regular function valued in the space of 3 x 3 positive definite matrix, which is the identity outside a compact set of R-3. (C) Academie des Sciences/Elsevier, Paris.

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