Abstract
This paper is concerned with the multidimensional pulsating waves and spreading speed for a class of reaction–advection–diffusion equations with degenerate monostable nonlinearity in space–time periodic media. Firstly, we show that the pulsating wave with the critical speed is unique up to translation, monotone and decays to zero exponentially, while the pulsating waves with noncritical speeds decay to zero nonexponentially. Then, combining the super- and sub-solution method and the asymptotic behavior of the pulsating waves, it is proved that the spreading speed of the degenerate monostable equations with compactly supported initial data is characterized by the critical speed under appropriate assumptions.
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