366,455 research outputs found
Transition Fronts in Time Heterogeneous and Random Media of Ignition Type
The current paper is devoted to the investigation of wave propagation
phenomenon in reaction-diffusion equations with ignition type nonlinearity in
time heterogeneous and random media. It is proven that such equations in time
heterogeneous media admit transition fronts or generalized traveling wave
solutions with time dependent profiles and that such equations in time random
media admit generalized traveling wave solutions with random profiles.
Important properties of generalized traveling wave solutions, including the
boundedness of propagation speeds and the uniform decaying estimates of the
propagation fronts, are also obtained
Stability, Uniqueness and Recurrence of Generalized Traveling Waves in Time Heterogeneous Media of Ignition Type
The present paper is devoted to the study of stability, uniqueness and
recurrence of generalized traveling waves of reaction-diffusion equations in
time heterogeneous media of ignition type, whose existence has been proven by
the authors of the present paper in a previous work. It is first shown that
generalized traveling waves exponentially attract wave-like initial data. Next,
properties of generalized traveling waves, such as space monotonicity and
exponential decay ahead of interface, are obtained. Uniqueness up to space
translations of generalized traveling waves is then proven. Finally, it is
shown that the wave profile of the unique generalized traveling wave is of the
same recurrence as the media. In particular, if the media is time almost
periodic, then so is the wave profile of the unique generalized traveling wave
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