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The Cauchy problem for wave equations with non Lipschitz coefficients; Application to continuation of solutions of some nonlinear wave equations. (English) Zbl 1172.35041

The well-posedness of the Cauchy problem for the second order strictly hyperbolic equations with Log-Lipschitz coefficients with respect to all variables, is studied. The main results refer to the local existence, local uniqueness and finite speed of propagation of the solution for the Cauchy problem, in some specific Sobolev spaces. The techniques of para-differential calculus von Bony are used. Much work is done for proving good energy estimates for the weak solution. In the last section, as an application, one shows a blow-up criterion for a nonlinear wave equation.

MSC:

35L15 Initial value problems for second-order hyperbolic equations
35L70 Second-order nonlinear hyperbolic equations
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