Nonexistence of Positive Nonconstant Stationary Solutions for Generalized Gray-Scott Model
نویسندگان
چکیده
منابع مشابه
Gray - Scott Model
In this paper, we rigorously prove the existence and stability of asymmetric spotty patterns for the Gray-Scott model in a bounded two dimensional domain. We show that given any two positive integers k 1 ; k 2 , there are asymmetric solutions with k 1 large spots (type A) and k 2 small spots (type B). We also give conditions for their location and calculate their heights. Most of these asymmetr...
متن کاملExistence and nonexistence of positive solutions for the fractional coupled system involving generalized p-Laplacian
In this article, we study a class of fractional coupled systems with Riemann-Stieltjes integral boundary conditions and generalized p-Laplacian which involves two different parameters. Based on the Guo-Krasnosel’skii fixed point theorem, some new results on the existence and nonexistence of positive solutions for the fractional system are received, the impact of the two different parameters on ...
متن کاملExistence and Stability of Multiple Spot Solutions for the Gray-scott Model in R2
In this paper, we rigorously prove the existence and stability of multiple spot patterns for the Gray-Scott system in a two dimensional domain which are far from spatial homogeneity. The Green's function together with its derivatives and two nonlocal eigenvalue problems both play a major role in the analysis. We establish a threshold behavior: If a certain inequality holds then we get stability...
متن کاملRise and Fall of Periodic Patterns for a Generalized Klausmeier-Gray-Scott Model
In this paper we introduce a conceptual model for vegetation patterns that generalizes the Klausmeier model for semi-arid ecosystems on a sloped terrain [23]. Our model not only incorporates downhill flow, but also linear or nonlinear diffusion for the water component. To relate the model to observations and simulations in ecology, we first consider the onset of pattern formation through a Turi...
متن کاملSpike autosolitons in the Gray-Scott model
We performed a comprehensive study of the spike autosolitons: self-sustained solitary inhomogeneous states, in the classical reaction-diffusion system — the GrayScott model. We developed singular perturbation techniques based on the strong separation of the length scales to construct asymptotically the solutions in the form of a one-dimensional static autosolitons, higher-dimensional radially-s...
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: Pure Mathematics
سال: 2016
ISSN: 2160-7583,2160-7605
DOI: 10.12677/pm.2016.66066