Global solutions to cross diffusion parabolic systems on 2D domains
نویسندگان
چکیده
منابع مشابه
Global attractors and uniform persistence for cross diffusion parabolic systems
A class of cross diffusion parabolic systems given on bounded domains of IR, with arbitrary n, is investigated. We show that there is a global attractor with finite Hausdorff dimension which attracts all solutions. The result will be applied to the generalized Shigesada, Kawasaki and Teramoto (SKT) model with Lotka-Volterra reactions. In addition, the persistence property of the SKT model will ...
متن کاملOn Global Existence of Solutions to a Cross-diffusion System
the Laplacian, ∂/∂ν denotes the directional derivative along the outward normal on ∂Ω, ai, bi, ci, di (i = 1, 2) are given positive constants and α, γ, δ, β are nonnegative constants. In the system (1.1) u and v are non-negative functions which represent population densities of two competing species, d1 and d2 are respectively their diffusion rates. Parameters a1 and a2 are intrinsic growth rat...
متن کاملClassical solutions of quasilinear parabolic systems on two dimensional domains
Using a classical theorem of Sobolevskii on equations of parabolic type in a Banach space and recently obtained results on elliptic operators with discontinuous coefficients including mixed boundary conditions we prove that quasilinear parabolic systems in diagonal form admit a local, classical solution in the space of p–integrable functions, for some p > 1, over a bounded two dimensional space...
متن کاملGlobal existence for semilinear reaction-diffusion systems on evolving domains.
We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially linear isotropically evolving domains. The results hold without any assumptions on the sign of the growth rate. The analysis is valid for many systems that comm...
متن کاملOn Asymptotic Behaviors of Solutions to Parabolic Systems Modelling Chemotaxis
This paper deals with large time behaviors of solutions to a Keller-Segel system which possesses self-similar solutions. By taking into account the invariant properties of the equation with respect to a scaling and translations, we show that suitably shifted self-similar solutions give more precise asymptotic profiles of general solutions at large time. The convergence rate is also computed in ...
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: Proceedings of the American Mathematical Society
سال: 2015
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2015-12501-4