We consider the Cauchy problem for a second order weakly hyperbolic equation, with coefficients depending only on the time variable. We prove that if the coefficients of the equation belong to the Gevrey class gs0s0 and the Cauchy data belong to gs1s1, then the Cauchy problem has a solution in gs0([0,T*];gs1(\mathbbR))s0([0T];s1(R)) for some T *>0, provided 1≤s 1≤2−1/s 0. If the equation is strictly hyperbolic, we may replace the previous condition by 1≤s 1≤s 0.
Time regularity of the solutions to second order hyperbolic equations
TAGLIALATELA, Giovanni
2011-01-01
Abstract
We consider the Cauchy problem for a second order weakly hyperbolic equation, with coefficients depending only on the time variable. We prove that if the coefficients of the equation belong to the Gevrey class gs0s0 and the Cauchy data belong to gs1s1, then the Cauchy problem has a solution in gs0([0,T*];gs1(\mathbbR))s0([0T];s1(R)) for some T *>0, provided 1≤s 1≤2−1/s 0. If the equation is strictly hyperbolic, we may replace the previous condition by 1≤s 1≤s 0.File in questo prodotto:
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