Global classical solutions for reaction–diffusion systems with nonlinearities of exponential growth
B Rebiai, S Benachour - Journal of Evolution Equations, 2010 - Springer
Journal of Evolution Equations, 2010•Springer
The aim of this study is to prove global existence of classical solutions for systems of the
form ∂ u ∂ ta Δ u=-f (u, v), ∂ v ∂ tb Δ v= g (u, v) in (0,+∞)× Ω where Ω is an open bounded
domain of class C 1 in R^ n, a> 0, b> 0 and f, g are nonnegative continuously differentiable
functions on 0,+∞)× 0,+∞) satisfying f (0, η)= 0, g (ξ, η) ≦ C φ (ξ) e^ α η^ β and g (ξ, η)≤ ψ
(η) f (ξ, η) for some constants C> 0, α> 0 and β≥ 1 where φ and ψ are any nonnegative
continuously differentiable functions on 0,+∞) such that φ (0)= 0 and η →+ ∞ η^ β-1 ψ (η)= ℓ …
form ∂ u ∂ ta Δ u=-f (u, v), ∂ v ∂ tb Δ v= g (u, v) in (0,+∞)× Ω where Ω is an open bounded
domain of class C 1 in R^ n, a> 0, b> 0 and f, g are nonnegative continuously differentiable
functions on 0,+∞)× 0,+∞) satisfying f (0, η)= 0, g (ξ, η) ≦ C φ (ξ) e^ α η^ β and g (ξ, η)≤ ψ
(η) f (ξ, η) for some constants C> 0, α> 0 and β≥ 1 where φ and ψ are any nonnegative
continuously differentiable functions on 0,+∞) such that φ (0)= 0 and η →+ ∞ η^ β-1 ψ (η)= ℓ …
Abstract
The aim of this study is to prove global existence of classical solutions for systems of the form , in (0, +∞) × Ω where Ω is an open bounded domain of class C 1 in , a > 0, b > 0 and f, g are nonnegative continuously differentiable functions on [0, +∞) × [0, +∞) satisfying f (0, η) = 0, and g(ξ, η) ≤ ψ(η)f(ξ, η) for some constants C > 0, α > 0 and β ≥ 1 where and ψ are any nonnegative continuously differentiable functions on [0, +∞) such that and where ℓ is a nonnegative constant. The asymptotic behavior of the global solutions as t goes to +∞ is also studied. For this purpose, we use the appropriate techniques which are based on semigroups, energy estimates and Lyapunov functional methods.
Springer
以上显示的是最相近的搜索结果。 查看全部搜索结果