Regular attractor for damped KdV‐Burgers equations on R |
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| Authors: | Yantao Guo Ming Wang |
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| Affiliation: | School of Mathematics and Statistics, Xuchang University, Xuchang, China |
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| Abstract: | We study the well‐posedness and dynamic behavior for the KdV‐Burgers equation with a force  on R . We establish L p ?L q estimates of the evolution  , as an application we obtain the local well‐posedness. Then the global well‐posedness follows from a uniform estimate for solutions as t goes to infinity. Next, we prove the asymptotical regularity of solutions in space  and  by the smoothing effect of  . The regularity and the asymptotical compactness in L 2 yields the asymptotical compactness in  by an interpolation arguement. Finally, we conclude the existence of an  globalattractor. |
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| Keywords: | Global attractor KdV‐Burgers equation Lpestimates |
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