相关论文: Completely exceptional $2^\textrm{nd}$ order PDEs …

The theory of perfect fluids is reconsidered from the point of view of a covariant Lagrangian theory. It has been shown that the Euler-Lagrange equations for a perfect fluid could be found in spaces with affine connections and metrics from…

We construct the exceptional sigma model: a two-dimensional sigma model coupled to a supergravity background in a manifestly (formally) $E_{D(D)}$-covariant manner. This formulation of the background is provided by Exceptional Field Theory…

Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…

In this article we study constrained variational problems in one independent variable defined on the space of integral curves of a Frenet system in a homogeneous space G/H. We prove that if the Lagrangian is G-invariant and coisotropic then…

We obtain uniqueness and existence of a solution $u$ to the following second-order stochastic partial differential equation (SPDE) : \begin{align} \label{abs eqn} du= \left( \bar a^{ij}(\omega,t)u_{x^ix^j}+ f \right)dt + g^k dw^k_t, \quad t…

We present the first method to directly use a learned continuous Lagrangian to forecast the dynamics of systems governed by partial differential equations, exploiting the inherent conservative structure to achieve stable long-range…

We introduce suitable coordinate systems for pipes and their variants that allow us to transform partial differential equations (PDEs) on the pipe surfaces or in the solid pipes into computational domains with fixed limits/ranges. Such a…

Let $(X,g)$ be a compact manifold with conic singularities. Taking $\Delta_g$ to be the Friedrichs extension of the Laplace-Beltrami operator, we examine the singularities of the trace of the half-wave group $e^{- i t \sqrt{…

We show how the exceptional isogenies of classical groups to orthogonal groups of quadratic spaces of dimensions up to 8 over fields of characteristic different from 2 may be obtained by explicit algebraic constructions using the…

We provide five examples of conformal geometries which are naturally associated with ordinary differential equations (ODEs). The first example describes a one-to-one correspondence between the Wuenschmann class of 3rd order ODEs considered…

The purpose of this work is to investigate the exponential stability of a second order coupled wave equations by laplacian with one locally internal viscous damping. Firstly, using a unique continuation theorem combined with a Carleman…

Blow-up in second and fourth order semi-linear parabolic partial differential equations (PDEs) is considered in bounded regions of one, two and three spatial dimensions with uniform initial data. A phenomenon whereby singularities form at…

We consider constrained bilinear optimal control of second-order linear evolution partial differential equations (PDEs) with a reaction term on the half line, where control arises as a time-dependent reaction coefficient and constraints are…

Some time ago, Thies et al. showed that the Gross-Neveu model with a bare mass term possesses a kink-antikink crystalline phase. Corresponding self-consistent solutions, known earlier in polymer physics, are described by a self-isospectral…

In this paper we give an explicit representation of the solutions of a characteristic Cauchy problem for a class of PDEs with singular coefficients. We give the explicit solutions in terms of the Gauss hypergeometric functions, which enable…

In this paper, we propose a procedure for constructing an infinite number of families of solutions of given linear differential equations with partial derivatives with constant coefficients. We use monogenic functions that are defined on…

It is shown that large classes of nonlinear systems of PDEs, with possibly associated initial and/or boundary value problems, can be solved by the method of order completion. The solutions obtained can be assimilated with Hausdorff…

Inspired by the classical Poincar\'e criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the variational properties of periodic…

We consider general symmetric systems of first order linear partial differential operators on domains $\Omega \subset \mathbb{R}^d$, and we seek sufficient conditions on the coefficients which ensure essential self-adjointness. The…

We revisit the problem of building the Lagrangian of a large class of metric theories that respect spatial covariance, which propagate at most two degrees of freedom and in particular no scalar mode. The Lagrangians are polynomials built of…