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

• Autorzy: Dirk Horstmann
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35K57: Reaction-diffusion equations
• 35K40: Second-order parabolic systems
• 35B40: Asymptotic behavior of solutions
• 35K55: Nonlinear parabolic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2001
• Tom: 87
• Numer: 1
• Strony: 113-127

Daty

wydano

2001

Twórcy

autor

Dirk Horstmann

• Mathematisches Institut, Universität zu Köln, Weyertal 86-90, D-50931 Köln, Germany

Identyfikatory

DOI

10.4064/cm87-1-7