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On the asymptotic behavior of solutions to the (generalized) Kadomtsev-Petviashvili-Burgers equations. (English) Zbl 0927.35095

This study deals with the temporal asymptotic decay of the solutions of the 2D-Kadomtsev-Petviashvili equations with a power nonlinearity \(u^p u_x\) and with a Burgers-type dissipation in the main \(x\)-direction. The basic result is that the decay of the \(L^2\)-norm of the solution is exactly the same as the decay of the solution of these equations linearized around the zero solution.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B40 Asymptotic behavior of solutions to PDEs
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