Related papers: New Algebraic Approaches to Classical Boundary Lay…
The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…
Lie-algebraic and quantum-algebraic techniques are used in the analysis of thermodynamic properties of molecules and solids. The local anharmonic effects are described by a Morse-like potential associated with the $su(2)$ algebra. A…
Nonlinear boundary value problems (BVPs) by means of the classical Lie symmetry method are studied. A new definition of Lie invariance for BVPs is proposed by the generalization of existing those on much wider class of BVPs. A class of…
We consider a nonlinear version of the Yamabe problem on locally conformally flat compact manifolds with boundary. The main technique we used is to derive boundary $C^2$ estimates directly from boundary $C^0$ estimates. In particular, the…
We prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for perturbed Hammerstein integral equations. Our approach is topological and relies on the classical fixed point index. Some of the…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
Using the 4th and the 3rd degree spherical harmonics as the representations for volumetric frames, we describe a simple algebraic technique for combining multiple frame orientation constraints into a single quadratic penalty function. This…
We consider the most general class of linear boundary-value problems for higher-order ordinary differential systems whose solutions and right-hand sides belong to the corresponding Sobolev spaces. For parameter-dependent problems from this…
The moving coframe method is applied to solve the local equivalence problem for the class of nonlinear wave equations in two independent variables under an action of the pseudo-group of contact transformations. The structure equations and…
In this paper we continue our study of bifurcations of solutions of boundary-value problems for symplectic maps arising as Hamiltonian diffeomorphisms. These have been shown to be connected to catastrophe theory via generating functions and…
This paper studies the boundary behaviour at mechanical equilibrium at the ends of a finite interval of a class of systems of interacting particles with monotone decreasing repulsive force. Our setting covers pile-ups of dislocations,…
The general spectral boundary value problem framework is utilized to restate boundary value problems of Poincare, Hilbert, and Riemann for harmonic and analytic functions in abstract operator-theoretic terms.
Here classes of moving boundary problems of Stefan-type for both an established non-linear evolution equation of cuspon theory and novel reciprocally linked solitonic equations are shown to be solvable via Painleve' II symmetry reduction.
In this paper, we present a general approach to obtain numerical schemes with good mesh properties for problems with moving boundaries, that is for evolving submanifolds with boundaries. This includes moving domains and surfaces with…
In this paper, the algebraic Bethe ansatz with periodic boundary conditions is used to investigate trigonometric vertex models associated with the fundamental representations of the non-exceptional Lie algebras. This formulation allow us to…
Laplace interpolation is a popular approach in image inpainting using partial differential equations. The classic approach considers the Laplace equation with mixed boundary conditions. Recently a more general formulation has been proposed…
The classical Lie method is applied to a nonisospectral problem associated with a system of partial differential equations in 2+1 dimensions (Maccari A, J. Math. Phys. 39, (1998), 6547-6551). Identification of the classical Lie symmetries…
This paper describes a novel numerical model aiming at solving moving-boundary problems such as free-surface flows or fluid-structure interaction. This model uses a moving-grid technique to solve the Navier--Stokes equations expressed in…
We prove convergence of piecewise polynomial collocation methods applied to periodic boundary value problems for functional differential equations with state-dependent delays. The state dependence of the delays leads to nonlinearities that…
The paper concerns classical solution of path-dependent partial differential equations (PPDEs) with coefficients depending on both variables of path and path-valued measure, which are crucial to understanding large-scale mean-field…