Stable small-amplitude solutions in reaction-diffusion systems
نویسندگان
چکیده
منابع مشابه
Large Stable Pulse Solutions in Reaction-diffusion Equations
In this paper we study the existence and stability of asymptotically large stationary multi-pulse solutions in a family of singularly perturbed reaction-diffusion equations. This family includes the generalized Gierer-Meinhardt equation. The existence of N-pulse homoclinic orbits (N ≥ 1) is established by the methods of geometric singular perturbation theory. A theory, called the NLEP (=NonLoca...
متن کاملAsymptotics of solutions in nA + nB → C reaction–diffusion systems
We analyze the long time behavior of initial value problems that model a process where particles of type A and B diffuse in some substratum and react according to nA + nB → C. The case n = 1 has been studied before; it presents nontrivial behavior on the reactive scale only. In this paper we discuss in detail the cases n > 3, and prove that they show nontrivial behavior on the reactive and the ...
متن کاملExistence of travelling wave solutions in delayed reaction–diffusion systems with applications to diffusion–competition systems
This paper is concerned with the existence of travelling wave solutions in a class of delayed reaction–diffusion systems without monotonicity, which concludes two-species diffusion–competition models with delays. Previous methods do not apply in solving these problems because the reaction terms do not satisfy either the so-called quasimonotonicity condition or non-quasimonotonicity condition. B...
متن کاملStable Foliations near a Traveling Front for Reaction Diffusion Systems
We establish the existence of a stable foliation in the vicinity of a traveling front solution for systems of reaction diffusion equations in one space dimension that arise in the study of chemical reactions models and solid fuel combustion. In this way we complement the orbital stability results from earlier papers by A. Ghazaryan, S. Schecter and Y. Latushkin. The essential spectrum of the di...
متن کاملParallel Solutions for Voxel-Based Simulations of Reaction-Diffusion Systems
There is an increasing awareness of the pivotal role of noise in biochemical processes and of the effect of molecular crowding on the dynamics of biochemical systems. This necessity has given rise to a strong need for suitable and sophisticated algorithms for the simulation of biological phenomena taking into account both spatial effects and noise. However, the high computational effort charact...
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: Quarterly of Applied Mathematics
سال: 1981
ISSN: 0033-569X,1552-4485
DOI: 10.1090/qam/613952