Dispersive limit from the Kawahara to the KdV equation
نویسندگان
چکیده
We investigate the limit behavior of the solutions to the Kawahara equation ut + u3x + εu5x + uux = 0 , ε > 0 as ε → 0. In this equation, the terms u3x and εu5x do compete together and do cancel each other at frequencies of order 1/ √ ε. This prohibits the use of a standard dispersive approach for this problem. Nervertheless, by combining different dispersive approaches according to the range of spaces frequencies, we succeed in proving that the solutions to this equation converges in C([0, T ];H(R)) towards the solutions of the KdV equation for any fixed T > 0.
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