Related papers: New Results on Compact Structures
We study a one-dimensional ordinary differential equation modelling optical conveyor belts, showing in particular cases of physical interest that periodic solutions exist. Moreover, under rather general assumptions it is proved that the set…
In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…
For the nonlinear Dirac equation with scalar self-interaction (the Soler model) in three spatial dimensions, we consider the linearization at solitary wave solutions and find the invariant spaces which correspond to different spherical…
This paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping. We study the case where the damping is effective in a well-chosen subset of arbitrarily small measure.
Periodic solutions of delay equations are usually approximated as continuous piecewise polynomials on meshes adapted to the solutions' profile. In practical computations this affects the regularity of the (coefficients of the) linearized…
In recent years the topic of localized wave solutions of the homogeneous scalar wave equation, i.e., the wave fields that propagate without any appreciable spread or drop in intensity, has been discussed in many aspects in numerous…
In this paper we consider the linearized version of a system of partial differential equations arising from a fluid-structure interaction model. We prove the existence and the uniqueness of the solution under natural regularity assumptions.
We perform a systematic analysis of the conditions under which \textit{generalized} gauge field theories of compact semisimple Lie groups exhibit electrostatic spherically symmetric non-topological soliton solutions in three space…
We prove that if a linear equation, whose coefficients are continuous rational functions on a nonsingular real algebraic surface, has a continuous solution, then it also has a continuous rational solution. This is known to fail in higher…
We study the stability of topological structures in generalized models with a single real scalar field. We show that it is driven by a Sturm-Liouville equation and investigate the conditions that lead to the existence of explicit…
We study solutions of the system of PDE $D\psi({\bf v}_t)=\text{div}DF(D{\bf v})$, where $\psi$ and $F$ are convex functions. This type of system arises in various physical models for phase transitions. We establish compactness properties…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
The paper proves existence of renormalized solutions for a class of velocity-discrete coplanar stationary Boltzmann equations with given indata. The proof is based on the construction of a sequence of approximations with L1 compactness for…
In this manuscript we systematically review known results of local dynamics of discrete local holomorphic dynamics near fixed points in one and several complex variables as well as the consequences in global dynamics.
This perspective deals with real scalar fields in two-dimensional spacetime. We focus on models described by one and two real scalar fields, paying closer attention to kinks and lumps, which are localized structures of current interest in…
We investigate stationary solutions of a non-local aggregation equation with degenerate power-law diffusion and bounded attractive potential in arbitrary dimensions. Compact stationary solutions are characterized and compactness…
We study the spatial-homogeneity of stable solutions of almost-periodic parabolic equations. It is shown that if the nonlinearity satisfies a concave or convex condition, then any linearly stable almost automorphic solution is…
We describe a map-based model which reproduces many of the behaviors seen in partial differential equations (PDE's). Like PDE's, we show that this model can support an infinite number of stationary solutions, traveling solutions, breathing…
Local and global phase-space descriptions and averaging methods are used to find qualitative features of solutions for the FLRW and the Bianchi I metrics in the context of scalar field cosmologies with arbitrary potentials and arbitrary…
We show that if the probabilistic logarithmic-space solver or the deterministic nearly logarithmic-space solver for undirected Laplacian matrices can be extended to solve slightly larger subclasses of linear systems, then they can be use to…