Local Existence And Stability Results For A Wave Equation With Damping On All R
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چکیده
We discuss the local existence results of the solutions for the nonlocal hyperbolic problem 2 ( ) || ( ) || ( ) 0, tt t u x u t u u , N x R 0, t with initial conditions 0 ( ,0) ( ) u x u x and 1 ( ,0) ( ), t u x u x in the case where 3, 0 N and 1 ( ( )) ( ) x g x is a positive function lying in / ( ) ( ). N N N L R L R When the initial energy 0 1 ( , ) E u u which corresponds to the problem, is non-negative and small, there exists a unique local solution in time. Keywords—Quasilinear Hyperbolic Equations, Unbounded Domains, Generalized Sobolev Spaces.
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