Lyapunov functions and $L^p$-estimates for a class of reaction-diffusion systems

Dirk Horstmann. "Lyapunov functions and $L^{p}$-estimates for a class of reaction-diffusion systems." Colloquium Mathematicae 87.1 (2001): 113-127. <http://eudml.org/doc/283757>.

@article{DirkHorstmann2001,
abstract = {We give a sufficient condition for the existence of a Lyapunov function for the system aₜ = ∇(k(a,c)∇a - h(a,c)∇c), x ∈ Ω, t > 0, $εcₜ = k_\{c\}Δc - f(c)c + g(a,c)$, x ∈ Ω, t > 0, for $Ω ⊂ ℝ^\{N\}$, completed with either a = c = 0, or ∂a/∂n = ∂c/∂n = 0, or k(a,c) ∂a/∂n = h(a,c) ∂c/∂n, c = 0 on ∂Ω × t > 0. Furthermore we study the asymptotic behaviour of the solution and give some uniform $L^\{p\}$-estimates.},
author = {Dirk Horstmann},
journal = {Colloquium Mathematicae},
keywords = {asymptotic behaviour of solution; uniform -estimates},
language = {eng},
number = {1},
pages = {113-127},
title = {Lyapunov functions and $L^\{p\}$-estimates for a class of reaction-diffusion systems},
url = {http://eudml.org/doc/283757},
volume = {87},
year = {2001},
}

TY - JOUR
AU - Dirk Horstmann
TI - Lyapunov functions and $L^{p}$-estimates for a class of reaction-diffusion systems
JO - Colloquium Mathematicae
PY - 2001
VL - 87
IS - 1
SP - 113
EP - 127
AB - We give a sufficient condition for the existence of a Lyapunov function for the system aₜ = ∇(k(a,c)∇a - h(a,c)∇c), x ∈ Ω, t > 0, $εcₜ = k_{c}Δc - f(c)c + g(a,c)$, x ∈ Ω, t > 0, for $Ω ⊂ ℝ^{N}$, completed with either a = c = 0, or ∂a/∂n = ∂c/∂n = 0, or k(a,c) ∂a/∂n = h(a,c) ∂c/∂n, c = 0 on ∂Ω × t > 0. Furthermore we study the asymptotic behaviour of the solution and give some uniform $L^{p}$-estimates.
LA - eng
KW - asymptotic behaviour of solution; uniform -estimates
UR - http://eudml.org/doc/283757
ER -