论文标题
具有不同速度的多组分反应扩散 - 添加系统中的全球存在和衰减：时间和频率的振荡
Global existence and decay in multi-component reaction-diffusion-advection systems with different velocities: oscillations in time and frequency
论文作者
论文摘要
众所周知，反应扩散 - 辅助系统中的二次或立方非线性可以导致具有小的，局部初始数据甚至有限的时间爆炸的溶液的增长。然而，最近证明，如果两个非线性耦合反应 - 扩散 - 添加方程的成分以不同的速度传播，则可以二次或立方混合过程，即〜非线性术语，与两个组成部分的非平凡贡献，不会影响全球存在和高斯的生存和高斯的小衰减。证明依赖于点估计来捕获速度的差异。在本文中，我们提出了一种替代方法，该方法更适用于多个组件。我们的方法涉及一种非线性迭代方案，该方案在傅立叶空间中采用$ l^1 $ - $ l^p $估计，并利用时间和频率的振荡，这是由于运输差异而引起的。在每个组件都表现出不同速度的假设下，我们在多组分反应 - 扩散 - 添加系统中建立了全局的存在和衰减，允许立方混合过程和汉堡类型的非线性条款。
It is well-known that quadratic or cubic nonlinearities in reaction-diffusion-advection systems can lead to growth of solutions with small, localized initial data and even finite time blow-up. It was recently proved, however, that, if the components of two nonlinearly coupled reaction-diffusion-advection equations propagate with different velocities, then quadratic or cubic mixed-terms, i.e.~nonlinear terms with nontrivial contributions from both components, do not affect global existence and Gaussian decay of small, localized initial data. The proof relied on pointwise estimates to capture the difference in velocities. In this paper we present an alternative method, which is better applicable to multiple components. Our method involves a nonlinear iteration scheme that employs $L^1$-$L^p$ estimates in Fourier space and exploits oscillations in time and frequency, which arise due to differences in transport. Under the assumption that each component exhibits different velocities, we establish global existence and decay for small, algebraically localized initial data in multi-component reaction-diffusion-advection systems allowing for cubic mixed-terms and nonlinear terms of Burgers' type.
