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Mass-conserving reaction-diffusion (MCRD) systems are widely used to model phase separation and pattern formation in cell polarity, biomolecular condensates, and ecological systems. Numerical simulations and formal asymptotic analysis…
In this work, we present a variational and quantitative phase-field model for non-isothermal sintering processes. The model is derived via an extended non-diagonal phase-field model. The model evolution equations have naturally…
We study the electrostatics of a thin, finite-length conducting cylindrical shell held at constant potential V0. Exploiting axial symmetry, we recast the problem as a one-dimensional singular integral equation for the axial surface-charge…
Convergence to stationary solutions in fully nonlinear parabolic systems with general nonlinear boundary conditions is shown in situations where the set of stationary solutions creates a $C^2$-manifold of finite dimension which is normally…
A closed-form solution for the boundary of the flat state of an orthogonal cross section of contiguous surface geometry formed by the intersection of two cylinders of equal radii oriented in dual directions of rotation about their…
We study partial H\"older regularity for nonlinear elliptic systems in divergence form with double-phase growth, modeling double-phase non-Newtonian fluids in the stationary case.
In this article, we investigate electrostatic systems with a nonzero cosmological constant on compact manifolds with boundary. We establish new geometric properties for electrostatic manifolds in higher dimensions, extending previous…
We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are…
A methodology is presented for the numerical solution of nonlinear elliptic systems in unbounded domains, consisting of three elements. First, the problem is posed on a finite domain by means of a proper nonlinear change of variables. The…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
We prove the global in time existence of spherically symmetric solutions to an initial-boundary value problem for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear,…
The transition from two-dimensional to three-dimensional flows in a finite circular cylinder driven by an axially oscillating sidewall is explored in detail. The complete symmetry group of this flow, including a spatio-temporal symmetry…
We study the growth of a periodic pattern in one dimension for a model of spinodal decomposition, the Cahn-Hilliard equation. We particularly focus on the intermediate region, where the non-linearity cannot be negected anymore, and before…
We consider electromagnetic nonlinear normal modes in cylindrical cavity resonators filled with a nonlinear nondispersive medium. The key feature of the analysis is that exact analytical solutions of the nonlinear field equations are…
This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of…
The present work aims to revisit the simplifications made in the Navier-Stokes equations for the flow between two cylinders with a small thickness of lubricating oil film. Through a dimensionless analysis, the terms of these equations are…
We consider the heat equation in a multidimensional domain with nonlocal hysteresis feedback control in a boundary condition. Thermostat is our prototype model. We construct all periodic solutions with exactly two switching on the period…
Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of…
We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric.
Previous studies of chemotaxis models with consumption of the chemoattractant (with or without fluid) have not been successful in explaining pattern formation even in the simplest form of concentration near the boundary, which had been…