Multidimensional stability of planar travelling waves

Kapitula, Todd

doi:10.1090/S0002-9947-97-01668-1

Multidimensional stability of planar travelling waves
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Trans. Amer. Math. Soc. 349 (1997), 257-269 Request permission

Abstract:

The multidimensional stability of planar travelling waves for systems of reaction-diffusion equations is considered in the case that the diffusion matrix is the identity. It is shown that if the wave is exponentially orbitally stable in one space dimension, then it is stable for $x\in \mathbf {R}^n, n\ge 2$. Furthermore, it is shown that the perturbation of the wave decays like $t^{-(n-1)/4}$ as $t\to \infty$. The result is proved via an application of linear semigroup theory.

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