Existence and non-existence of transition fronts in mixed ignition-monostable media
نویسندگان
چکیده
منابع مشابه
Existence and Non-existence of Transition Fronts for Bistable and Ignition Reactions
We study reaction-diffusion equations in one spatial dimension and with general (spaceor time-) inhomogeneous mixed bistable-ignition reactions. For those satisfying a simple quantitative hypothesis, we prove existence and uniqueness of transition fronts, as well as convergence of “typical” solutions to the unique transition front (the existence part even extends to mixed bistable-ignition-mono...
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We consider Fisher-KPP-type reaction-diffusion equations with spatially inhomogeneous reaction rates. We show that a sufficiently strong localized inhomogeneity may prevent existence of transition-front-type global in time solutions while creating a global in time bump-like solution. This is the first example of a medium in which no reaction-diffusion transition front exists. A weaker localized...
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We consider a reaction-diffusion equation with a nonlinear term of the Fisher-KPP type, depending on time t and admitting two limits as t → ±∞. We derive the set of admissible asymptotic past and future speeds of transition fronts for such equation. We further show that any transition front which is non-critical as t → −∞ always admits two asymptotic past and future speeds. We finally describe ...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2018
ISSN: 0951-7715,1361-6544
DOI: 10.1088/1361-6544/aa952c