Existence and Uniqueness of Solutions for a Quasilinear KdV Equation with Degenerate Dispersion
Existence and Uniqueness of Solutions for a Quasilinear KdV Equation with Degenerate Dispersion
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简并色散拟线性KdV方程解的存在唯一性
DOI：
10.1002/cpa.21828
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发表时间：
2019
影响因子：
3
通讯作者：
Marzuola, Jeremy L.
中科院分区：
文献类型：
--
作者：
Germain, Pierre;Harrop‐Griffiths, Benjamin;Marzuola, Jeremy L.
考虑一类准线性KdV方程，它具有紧支撑行波解.这种模型是简并弥散的最直接的例子之一，这种现象出现在各种不同的物理环境中，如沉积，岩浆动力学和浅水波。我们证明了充分光滑，空间局部化的初始数据的解决方案的存在性和唯一性。© 2019 Wiley Periodicals，Inc.
We consider a quasilinear KdV equation that admits compactly supported traveling wave solutions (compactons). This model is one of the most straightforward instances of degenerate dispersion, a phenomenon that appears in a variety of physical settings as diverse as sedimentation, magma dynamics and shallow water waves. We prove the existence and uniqueness of solutions with sufficiently smooth, spatially localized initial data. © 2019 Wiley Periodicals, Inc.