On the Asymptotic Behavior of Solutions to the (Generalized) Kadomtsev–Petviashvili–Burgers Equations☆
On the Asymptotic Behavior of Solutions to the (Generalized) Kadomtsev–Petviashvili–Burgers Equations☆
复制标题
(广义)Kadomtsev-Petviashvili-Burgers 方程解的渐近行为☆
DOI：
10.1006/jdeq.1998.3522
复制
发表时间：
1999
期刊：
影响因子：
--
通讯作者：
L. Molinet
中科院分区：
文献类型：
--
作者：
L. Molinet
我们证明了具有幂次非线性项的广义KP方程解的整体存在性和渐近衰减性，并在主传播方向上附加Burgers型耗散.此外，我们证明了对于p ∈N*，这些方程解的L2-范数的衰减率是这些方程在零解附近线性化的解所表现的衰减率，并且对于p ∈ N *，这也适用于L ∞-范数。这种限制似乎是由于在横向上存在色散效应。
We show global existence and sharp results on the asymptotic decay of solutions to the generalized KP equations with a power nonlinearityupuxand with a Burgers-type dissipation in the main direction of propagation appended. Furthermore, we prove that forp∈N* the decay rate of theL2-norm of the solution of these equations is that exhibited by the solution of these same equations linearized around the zero solution and that, forp⩾2, this also holds for theL∞-norm. This limitation seems due to the presence of a dispersive effect in the transverse direction.