Related papers: Shadowing for differential equations with grow-up
The so-called method of phase synchronization has been advocated in a number of papers as a way of decoupling a system of linear second-order differential equations by a linear transformation of coordinates and velocities. This is a rather…
The mixed problem for the implicit degenerating nonlinear parabolic equation is considered, and the solvability and behavior of solutions of this problem are studied. Furthermore, some classes of function spaces and their relations with…
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…
We consider divergence form uniformly parabolic SPDEs with bounded and measurable leading coefficients and possibly growing lower-order coefficients in the deterministic part of the equations. We look for solutions which are summable to the…
A straight-forward extension of the Jackson-Hunt theory for directionally solidifying multi-phase growth where the number of components exceeds the number of solid phases becomes difficult on account of the absence of the required number of…
In this paper we revisit a Poincare lemma for foliated forms, with respect to a regular foliation, and compute the foliated cohomology for local models of integrable systems with singularities of nondegenerate type. A key point in this…
For any continuous self-map of a compact metric space, we consider the space of chain components and prove that the s-limit shadowing implies the denseness of chain components with the shadowing property. It gives a partial answer to a…
This article provides the second part of the research initiated in arXiv:2411.17381, where we introduced and investigated so called periodicity shadows, which are special skew-symmetric matrices related to symmetric algebras with periodic…
We prove the self-improving property of very weak solutions to non-uniformly elliptic problems of double phase type in divergence form under sharp assumptions on the nonlinearity.
We introduce the notion of conditional Lipschitz shadowing, which does not aim to shadow every pseudo-orbit, but only those which belong to a certain prescribed set. We establish two types of sufficient conditions under which certain…
We extend Deligne's weight filtration to the integer cohomology of complex analytic spaces (endowed with an equivalence class of compactifications). In general, the weight filtration that we obtain is not part of a mixed Hodge structure.…
The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are…
Regularity properties of the pressure are related to phase transitions. In this article we study thermodynamic formalism for systems defined in non-compact phase spaces, our main focus being countable Markov shifts. We produce metric…
This paper studies the equivalence between differentiable and non-differentiable dynamics in Rn. Filippov's theory of discontinuous differential equations allows us to find flow solutions of dynamical systems whose vector fields undergo…
The impact of a wedge-shaped body on the free surface of a weightless inviscid incompressible liquid is considered. Both symmetrical and unsymmetrical entries at constant velocity are dealt with. The differential problem corresponds to the…
We study weighted porous media equations on domains $\Omega\subseteq{\mathbb R}^N$, either with Dirichlet or with Neumann homogeneous boundary conditions when $\Omega\not={\mathbb R}^N$. Existence of weak solutions and uniqueness in a…
Demiclosedness principles are powerful tools in the study of convergence of iterative methods. For instance, a multi-operator demiclosedness principle for firmly nonexpansive mappings is useful in obtaining simple and transparent arguments…
In this paper we show that the introduction of an attenuation factor in the %image irradiance brightness equations relative to various perspective Shape from Shading models allows to make the corresponding differential problems well-posed.…
Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…
For nonautonomous linear difference equations, we introduce the notion of the so-called nonuniform dichotomy spectrum and prove a spectral theorem. Moreover, we introduce the notion of weak kinematical similarity and prove a reducibility…