Asymptotic behaviour of a population model with local, concave growth on Lipschitz domains

作者：Bernhard Manuel^*

来源：Journal of Mathematical Analysis and Applications, 2016, 439(1): 1-31.

DOI：10.1016/j.jmaa.2016.02.045

• Bifurcation
• Semilinear evolution equation
• Population model
• Lipschitz domain
• Local functions
• Long-term behavior

We examine the asymptotic behaviour of (u)over dot = dAu + f(u) for positive initial values u(0) > 0. Here A is the generator of an exponentially bounded semigroup on L-infinity (Omega) with several additional properties. A particular example is the Laplace operator A(Omega)(R,infinity) with Robin boundary conditions on a Lipschitz domain defined on L-infinity (Omega). Moreover, f : L-infinity (Omega) -> L-infinity (Omega) is a local, continuously Frechet-differentiable, and strictly concave map with f (0) = 0. We will analyse the asymptotic behaviour of the solutions as t -> infinity and its dependency on the diffusion coefficient t -> 0.

• 出版日期2016-7-1