Related papers: On a general variational framework for existence a…
The study of stochastic variational principles involves the problem of constructing fixed-endpoint and adapted variations of semimartingales. We provide a detailed construction of variations of semimartingales that are not only fixed at…
We formulate symmetric versions of classical variational principles. Within the framework of non-smooth critical point theory, we detect Palais-Smale sequences with additional second order and symmetry information. We discuss applications…
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…
We use a variational principle to prove an existence and uniqueness theorem for planar weighted Delaunay triangulations (with non-intersecting site-circles) with prescribed combinatorial type and circle intersection angles. Such weighted…
The article treats the geometrical theory of partial differential equations in the absolute sense, i.e., without any additional structures and especially without any preferred choice of independent and dependent variables. The equations are…
A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…
In this paper, we propose simple numerical algorithms for partial differential equations (PDEs) defined on closed, smooth surfaces (or curves). In particular, we consider PDEs that originate from variational principles defined on the…
The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate.…
A covariant, global, variational framework for perturbations in field theories is presented. Perturbations are obtained as vertical vector fields on the configuration bundle and they drag, exactly, solution into solutions. The flow of a…
As is known, the problems for the differential equations with continuously changing order of the derivatives are not considered completely. In this paper we consider the initial and boundary value problems for this type of linear ordinary…
Variational principles are proved for self-adjoint operator functions arising from variational evolution equations of the form \[ \langle\ddot{z}(t),y \rangle + \mathfrak{d}[\dot{z} (t), y] + \mathfrak{a}_0 [z(t),y] = 0. \] Here…
While exploring dynamical systems, we often come across the principle of contraction mapping, or better known as the Banach fixed point theorem. It is an essential concept based on successive approximation, whose utility comes from two main…
This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination…
We consider a variational approach to solve parabolic problems by minimising a functional over time and space. To achieve existence results we investigate the notion of $\mathscr{A}$-quasiconvexity for non-homogeneous operators in…
The quasi-variational inequalities play a significant role in analyzing a wide range of real-world problems. However, these problems are more complicated to solve than variational inequalities as the constraint set is based on the current…
Many partial differential equations (PDEs) such as Navier--Stokes equations in fluid mechanics, inelastic deformation in solids, and transient parabolic and hyperbolic equations do not have an exact, primal variational structure. Recently,…
The nonlinear selfdual variational principle established in a preceeding paper [8] -- though good enough to be readily applicable in many stationary nonlinear partial differential equations -- did not however cover the case of nonlinear…
In this paper we aim to combine tools from variational calculus with modern techniques from quaternionic analysis that involve Dirac type operators and related hypercomplex integral operators. The aim is to develop new methods for showing…
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…
The variational principle for the special and general relativistic hydrodynamics are discussed in view of its application to obtain approximate solutions to these problems. We show that effective Lagrangians can be obtained for suitable…