Related papers: Variational principles for nonlinear Kirchhoff rod…
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…
This article develops a new primal dual formulation for the Kirchhoff-Love non-linear plate model. At first we establish a duality principle which includes sufficient conditions of global optimality through the dual formulation. At this…
A dual variational principle is defined for the nonlinear system of PDE describing the dynamics of dislocations in elastic solids. The dual variational principle accounting for a specified set of initial and boundary conditions for a…
A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but…
In this paper, existence of solutions is established for critical exponential Kirchhoff systems on the Heisenberg group by using the variational method. The novelty of our paper is that not only the nonlinear term has critical exponential…
We present a new exact solution for the twist of an asymmetric thin elastic rods. The shape of such rods is described by the static Kirchhoff equations. In the case of constant curvatire and torsion the twist of the asymmetric rod…
Direct current (DC) circuits are usually taught in upper-level physics curricula, and Kirchhoff's laws are stated and used to solve the steady-state currents. However, students are not often introduced to alternative techniques, such as…
We use the entropy method to analyze the nonlinear dynamics and stability of a continuum kinetic model of an active nematic suspension. From the time evolution of the relative entropy -- an energy-like quantity in the kinetic model -- we…
This article develops dual variational formulations for a large class of models in variational optimization. The results are established through basic tools of functional analysis, convex analysis and duality theory. The main duality…
This article concerns on the existence of multiple solutions for a new Kirchhoff-type problem with negative modulus. We prove that there exist three nontrivial solutions when the parameter is enough small via the variational methods and…
Using Onsager's variational principle, we derive dynamical equations for a nonequilibrium active system with odd elasticity. The elimination of the extra variable that is coupled to the nonequilibrium driving force leads to the…
We formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting…
We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear differential equations assuming a very general form of dichotomic behavior for the linear equation. Besides some new…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
The first part of this article develops a variational formulation for relativistic mechanics. The results are established through standard tools of variational analysis and differential geometry. The novelty here is that the main motion…
In this work, we give a variation of parameters formula for nonautonomous linear impulsive differential equations with piecewise constant arguments of generalized type. We cover several cases of differential equations with deviated…
The study of vortex dynamics using a variational formulation has an extensive history and a rich literature. The standard Hamiltonian function that describes the dynamics of interacting point vortices of constant strength is the…
In this work, we investigate the application of an advanced nonlinear torsion- and shear-free Kirchhoff rod model, enhanced with a penalty-based barrier function (to simulate the seabed contact), intended for studying the static and dynamic…
Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. We show its potentiality with some…
We study the evolution of fronts in the Klein-Gordon equation when the nonlinear term is non-homogeneous. Extending previous works on homogeneous nonlinear terms, we describe the derivation of an equation governing the front motion, which…