Related papers: Quasi-Static BMN Solutions
This paper studies systems of linear difference equations on the lattice $\Z^n$ that are invariant under a finite group of symmetries, and shows that there exist solutions to such systems that are also invariant under this group of…
The concept of quasi-exact solutions of nonlinear differential equations is introduced. Quasi-exact solution expands the idea of exact solution for additional values of parameters of differential equation. These solutions are approximate…
We study differential expressions related to linear families of quasiconformal mappings and give a simple and direct proof to a result due to Alessandrini and Nesi arXiv:0707.0727.
In this paper Quintic Spline is defined for the numerical solutions of the fourth order linear special case Boundary Value Problems. End conditions are also derived to complete the definition of spline.The algorithm developed approximates…
In this paper we consider the spatial semi-discretization of conservative PDEs. Such finite dimensional approximations of infinite dimensional dynamical systems can be described as flows in suitable matrix spaces, which in turn leads to the…
We discuss existence of mixed state of multicomponent system with given spectrum and given reduced density matrices. We give a complete solution of the problem in terms of linear inequalities on the spectra, accompanied with extensive…
This course introduces the use of semigroup methods in the solution of linear and nonlinear (quasi-linear) hyperbolic partial differential equations, with particular application to wave equations and Hermitian hyperbolic systems. Throughout…
We study continuous quadratic submodular minimization with bounds and propose a polynomially sized semidefinite relaxation, which is provably tight for dimension $n \le 3$ and empirically tight for larger $n$. We apply the relaxation to two…
We are concerned with the energy equality for weak solutions to Newtonian and non-Newtonian incompressible fluids. In particular, the results obtained for non-Newtonian fluids, after restriction to the Newtonian case, equal or improve the…
For a wave equation with pure delay, we study an inhomogeneous initial-boundary value problem in a bounded 1D domain. Under smoothness assumptions, we prove unique existence of classical solutions for any given finite time horizon and give…
Partial differential equations (PDEs) are at the heart of many mathematical and scientific advances. While great progress has been made on the theory of PDEs of standard types during the last eight decades, the analysis of nonlinear PDEs of…
Integrable systems on quantum groups are investigated. The Heisenberg equations possessing the Lax form are solved in terms of the solution to the factorization problem on the corresponding quantum group.
A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.
The problem of membrane topology in the matrix model of M-theory is considered. The matrix regularization procedure, which makes a correspondence between finite-sized matrices and functions defined on a two-dimensional base space, is…
This survey on stationary and evolutionary problems with gradient constraints is based on developments of monotonicity and compactness methods applied to large classes of scalar and vectorial solutions to variational and quasi-variational…
In this work, we introduce the notion of regularization of bifunctions in a similar way as the well- known convex, quasiconvex and lower semicontinuous regularizations due to Crouzeix. We show that the Equilibrium Problems associated to…
A large family of linear, usually overdetermined, systems of partial differential equations that admit a multiplication of solutions, i.e, a bi-linear and commutative mapping on the solution space, is studied. This family of PDE's contains…
In this paper we study about the existence of solutions of certain kind of non-linear differential and differential-difference equations. We give partial answer to a problem which was asked by chen et al. in [13].
It is shown that a large subset of initial data with finite energy ($L^2$ norm)evolves nearly linearly in nonlinear Schr\" odinger equation with periodic boundary conditions. These new solutions are not perturbations of the known ones such…
In this paper we present some very recent results regarding existence, uniqueness, and multiplicity of solutions for quasilinear elliptic equations and systems, exhibiting both singular and convective reaction terms. The importance of…