Related papers: Semigroups and Evolutionary Equations
The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a…
We consider the Maxwell-Lorentz equations, i.e., the equation of motion of a charged dust coupled to Maxwell's equations, on an arbitrary general-relativistic spacetime. We decompose this system of equations into evolution equations and…
We present a new and very short proof of the fact that, for positive $C_0$-semigroups on spaces of continuous functions, the spectral and the growth bound coincide. Our argument, inspired by an idea of Vogt, makes the role of the underlying…
We consider infinite-dimensional parabolic rough evolution equations. Using regularizing properties of analytic semigroups we prove global-in-time existence of solutions and investigate random dynamical systems for such equations.
We present a generation theorem for positive semigroups on an $L^1$ space. It provides sufficient conditions for the existence of positive and integrable solutions of initial-boundary value problems. An application to a two-phase cell cycle…
Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which…
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…
Hyperbolic partial differential equations on a one-dimensional spatial domain are studied. This class of systems includes models of beams and waves as well as the transport equation and networks of non-homogeneous transmission lines. The…
Under the assumption that the infinite product of evolution process converges almost surely, the set of strong solutions are characterized by a compact space, which may be regarded as the set of possible initial states.
This paper is concerned with an evolution problem having an elliptic equation involving the 1-Laplacian operator and a dynamical boundary condition. We apply nonlinear semigroup theory to obtain existence and uniqueness results as well as a…
The issue of so-called maximal regularity is discussed within a Hilbert space framework for a class of evolutionary equations. Viewing evolutionary equations as a sums of two unbounded operators, showing maximal regularity amounts to…
The solution of an initial-boundary value problem for a linear evolution partial differential equation posed on the half-line can be represented in terms of an integral in the complex (spectral) plane. This representation is obtained by the…
We prove that any evolution equation admitting a potential symmetry can always be reduced to another evolution equation such that the potential symmetry in question maps into the group of its contact symmetries. Based on this fact is out…
We suggest the method for group classification of evolution equations admitting nonlocal symmetries which are associated with a given evolution equation possessing nontrivial Lie symmetry. We apply this method to second-order evolution…
We consider abstract evolution equations with a nonlinear term depending on the state and on delayed states. We show that, if the $C_0$-semigroup describing the linear part of the model is exponentially stable, then the whole system retains…
We discuss the issue of maximal regularity for evolutionary equations with non-autonomous coefficients. Here evolutionary equations are abstract partial-differential algebraic equations considered in Hilbert spaces. The catch is to consider…
We consider linear age-structured population equations with diffusion. Supposing maximal regularity of the diffusion operator, we characterize the generator and its spectral properties of the associated strongly continuous semigroup. In…
We prove that evolution families on complex complete hyperbolic manifolds are in one to one correspondence with certain semicomplete non-autonomous holomorphic vector fields, providing the solution to a very general Loewner type…
We consider several classes of degenerate hyperbolic equations involving delay terms and suitable nonlinearities. The idea is to rewrite the problems in an abstract way and, using semigroup theory and energy method, we study well posedness…
Each semigroup describing the time evolution of an open quantum system on a finite dimensional Hilbert space is related to a special structure of this space. It is shown how the space can be decomposed into subspaces: One is related to…