Nevanlinna domains with large boundaries

Swarm Equilibria in Domains with Boundaries

We study equilibria in domains with boundaries for a first-order aggregation model that includes social interactions and exogenous forces. Such equilibrium solutions can be connected or disconnected, the latter consisting in a delta concentration on the boundary and a free swarm component in the interior of the domain. Equilibria are stationary points of an energy functional, and stable configu...

7A Diffusion in domains with switching boundaries

In the analysis of narrow escape problems in Sect. 7.2, we assumed that the holes in the boundary of the domain were always open. However, if we view each pore as a stochastically gated ion channel, for example, then one has the problem of analyzing the diffusion equation in a domain with a randomly switching boundary (or partial boundary). Such a scenario also arises in the case of membrane di...

p-approach in domains with smooth boundaries

We investigate the steady transport equation λz + w · ∇z + az = f, λ > 0 in various domains (bounded or unbounded) with smooth noncompact boundaries. The functions w, a are supposed to be small in appropriate norms. The solution is studied in spaces of Sobolev type (classical Sobolev spaces, Sobolev spaces with weights, homogeneous Sobolev spaces, dual spaces to Sobolev spaces). The particular ...

Weakly Hyberbolic Equations in Domains with Boundaries

Universit at Konstanz Weakly Hyberbolic Equations in Domains with Boundaries Weakly Hyperbolic Equations in Domains with Boundaries

We consider weakly hyperbolic equations of the type u tt (t)+a(t)Au(t) = f(t; u(t)), u(0) = u 0 , u t (0) = u 1 ,u(t) 2 D(A), t 2 0; T], for a function u : 0; T] ?! H, T 2 0; 1], H a separable Hilbert space, A being a non-negative, self-adjoint operator with domain D(A). The real function a is assumed to be non-negative, continuous and (piecewise) continuous diierentiable, and the derivative a ...