Existence of Traveling Waves for the Generalized F–KPP Equation
نویسندگان
چکیده
منابع مشابه
Existence of traveling waves for the nonlocal Burgers equation
We study the equation ut + uux + u − K * u = 0 in the case of an arbitrary K ≥ 0, which is a generalization of a model for radiating gas, in which K(y) = 1 2 e −|y|. Using a monotone iteration scheme argument we establish the existence of traveling waves, which gives a solution to an open question raised by Denis Serre [1].
متن کاملGeneralized Traveling Waves in Disordered Media: Existence, Uniqueness, and Stability
We prove existence, uniqueness, and stability of transition fronts (generalized traveling waves) for reaction-diffusion equations in cylindrical domains with general inhomogeneous ignition reactions. We also show uniform convergence of solutions with exponentially decaying initial data to time translates of the front. In the case of stationary ergodic reactions the fronts are proved to propagat...
متن کاملTraveling Waves for the Whitham Equation
The existence of traveling waves for the original Whitham equation is investigated. This equation combines a generic nonlinear quadratic term with the exact linear dispersion relation of surface water waves of finite depth. It is found that there exist small-amplitude periodic traveling waves with sub-critical speeds. As the period of these traveling waves tends to infinity, their velocities ap...
متن کاملOn the Existence of Solitary Traveling Waves for Generalized Hertzian Chains
We consider the question of existence of “bell-shaped” (i.e. non-increasing for x > 0 and non-decreasing for x < 0) traveling waves for the strain variable of the generalized Hertzian model describing, in the special case of a p = 3/2 exponent, the dynamics of a granular chain. The proof of existence of such waves is based on the English and Pego [Proceedings of the AMS 133, 1763 (2005)] formul...
متن کاملExistence of supersonic traveling waves for the Frenkel-Kontorova model
In this paper, we study the standard one-dimensional (non-overdamped) Frenkel-Kontorova (FK) model describing the motion of atoms in a lattice. For this model we show that for any supersonic velocity c > 1, there exist bounded traveling waves moving with velocity c. The profile of these traveling waves is a phase transition between limit states k− in −∞ and k+ in +∞. Those limit states are some...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of Mathematical Biology
سال: 2016
ISSN: 0092-8240,1522-9602
DOI: 10.1007/s11538-016-0244-3