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In this paper, the growth-induced bending deformation of a thin hyperelastic plate is studied. For a plane-strain problem, the governing PDE system is formulated, which is composed of the mechanical equilibrium equations, the constraint…
We are concerned with the dynamical behavior of solutions to semilinear wave systems with time-varying damping and nonconvex force potential. Our result shows that the dynamical behavior of solution is asymptotically stable without any…
We consider a damped linear hyperbolic system modelling the propagation of pressure waves in a network of pipes. Well-posedness is established via semi-group theory and the existence of a unique steady state is proven in the absence of…
In this work, we establish local well-posedness for the Korteweg-de Vries model on a balanced star graph with a structure represented by semi-infinite edges, by considering a boundary condition of $\delta$-type at the {unique} graph-vertex.…
The aim of this work is to study the dynamics and stability of soft shape-morphing configurations and specifically the modes of interaction between the front and rear airfoil segments. Initially we present several steady-state solutions,…
We examine the dynamics of a particle in a general rotating quadratic potential, not necessarily stable or isotropic, using a general complex mode formalism. The problem is equivalent to that of a charged particle in a quadratic potential…
In this paper, we study the birational geometry of the Hilbert scheme of n points on P^2. We discuss the stable base locus decomposition of the effective cone and the corresponding birational models. We give modular interpretations to the…
Structural balance theory predicts that triads in networks gravitate towards stable configurations. The theory has been verified for undirected graphs. Since real-world networks are often directed, we introduce a novel method for…
This paper is addressed to a stabilization problem of a system coupled by a wave and a Euler-Bernoulli plate equation. Only one equation is supposed to be damped. Under some assumption about the damping and the coupling terms, it is shown…
The present paper is devoted to the study of existence, uniqueness and stability of transition fronts of nonlocal dispersal evolution equations in time heterogeneous media of bistable type under the unbalanced condition. We first study…
We consider a prototypical model in which a nonlinear field (continuum or discrete) evolves on a flexible substrate which feeds back to the evolution of the main field. We identify the underlying physics and potential applications of such a…
This is a short expository account of the regularity lemma for stable graphs proved by the authors, with some comments on the model theoretic context, written for a general logical audience.
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
We discuss the stability theory and numerical analysis of the Helmholtz equation with variable and possibly non-smooth or oscillatory coefficients. Using the unique continuation principle and the Fredholm alternative, we first give an…
We consider the cylindrical bending problem for an infinite plate as modelled with a family of generalized continuum models, including the micromorphic approach. The models allow to describe length scale effects in the sense that thinner…
It is recent that the emergence of topological insulators in condensed matter physics has inspired analogous wave phenomena in mechanical systems, mostly in the setting of discrete lattice models. Here we report a numerical and experimental…
We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…
Modulation instability in a nonlinear optical waveguide array with alternating positive and negative refractive indices is investigated analytically. Particular solutions of a system of coupled nonlinear equations are found. These solutions…
We prove that traveling waves in viscous compressible liquids are a generic phenomenon. The setting for our result is a horizontally infinite, finite depth layer of compressible, barotropic, viscous fluid, modeled by the free boundary…
For a class of scalar partial differential equations that incorporate convection, diffusion, and possibly dispersion in one space and one time dimension, the stability of traveling wave solutions is investigated. If the initial perturbation…