Related papers: A maximum principle for systems with variational s…
A more reasonable trial ground state wave function is constructed for the relative motion of an interacting two-fermion system in a 1D harmonic potential. At the boundaries both the wave function and its first derivative are continuous and…
We present a new variational principle for linking models of beams and deformable solids, providing also its mathematical analysis. Despite the apparent differences between the two types of governing equations, it will be shown that the…
The aim of this paper is to prove the existence of minimizers for a variational problem involving the minimization under volume constraint of the sum of the perimeter and a non-local energy of Wasserstein type. This extends previous partial…
We develop a new paradigm for finding bifurcations of solutions of nonlinear problems, which is based on the detection of extreme values of new type of variational functional associated with the considering problem. The variational…
Partial differential equations endowed with a Hamiltonian structure, like the Korteweg--de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for…
Noise-induced transitions between multistable states happen in a multitude of systems, such as species extinction in biology, protein folding, or tipping points in climate science. Large deviation theory is the rigorous language to describe…
We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…
This article is concerned with the mathematical analysis of a class of a nonlinear fractional Schrodinger equations with a general Hartree-type integrand. We prove existence and uniqueness of global-in-time solutions to the associated…
We study a Klein-Gordon-Maxwell system, in a bounded spatial domain, under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many standing…
A formal methodology for developing variational principles corresponding to a given nonlinear PDE system is discussed. The scheme is demonstrated in the context of the incompressible Navier-Stokes equations, systems of first-order…
We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter. Assuming the convexity of the control domain, we obtain the…
Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. Here, we study a broad class of bistable models subject to self-activation, degradation and spatially inhomogeneous activating agents. We…
This paper is devoted to proving the small noise asymptotic behaviour, particularly large deviation principle, for multi-scale stochastic dynamical systems with fully local monotone coefficients driven by multiplicative noise. The main…
Using an abstract scheme of monotone semiflows, the existence of bistable traveling wave solutions of a competitive recursion system with Ricker nonlinearity is established. The traveling wave solutions formulate the strong inter-specific…
We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced and is designed to handle independent…
Oscillons are localised long-lived pulsating states in the three-dimensional $\phi^4$ theory. We gain insight into the spatio-temporal structure and bifurcation of the oscillons by studying time-periodic solutions in a ball of a finite…
The periodic standing wave (PSW) method for the binary inspiral of black holes and neutron stars computes exact numerical solutions for periodic standing wave spacetimes and then extracts approximate solutions of the physical problem, with…
The focus of this study is on exploring some qualitative properties of solutions to a class of semilinear elliptic problems in bounded domains, where the boundary conditions depend non-locally on the unknown solution at specified interior…
By using variational methods, the existence of infinitely many solutions for a nonlinear algebraic system with a parameter is established in presence of a perturbed Lipschitz term. Our goal was achieved requiring an appropriate behavior of…
We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter…