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Euler-Poisson equations describe the temporal evolution of a rigid body's orientation through the rotation matrix and angular velocity components, governed by first-order differential equations. According to the Cauchy-Kovalevskaya theorem,…
We prove existence of solutions for a class of singular elliptic problems with a general measure as source term whose model is $$\begin{cases} -\Delta u = \frac{f(x)}{u^{\gamma}} +\mu & \text{in}\ \Omega, u=0 &\text{on}\ \partial\Omega, u>0…
We introduce a method for finding general solutions of third-order nonlinear differential equations by extending the modified Prelle-Singer method. We describe a procedure to deduce all the integrals of motion associated with the given…
In U. Nucamendi et al. Phys. Rev. D63 (2001) 125016 and K. Lake, Phys. Rev. Lett. 92 (2004) 051101 it has been shown that galactic potentials can be kinematically linked to the observed red/blue shifts of the corresponding galactic rotation…
In this paper, we are devoted to studying the positive weak, punctured or distributional solutions to the biharmonic Lane-Emden equation \begin{equation*} \Delta^{2} u=u^{p} \quad \quad \text{in} \ \mathbb{R}^{N}\setminus Z, \end{equation*}…
We study the Euclidean path integral of two-dimensional quantum gravity with positive cosmological constant coupled to conformal matter with large and positive central charge. The problem is considered in a semiclassical expansion about a…
We discuss dynamical systems approaches and methods applied to flat Robertson-Walker models in $f(R)$-gravity. We argue that a complete description of the solution space of a model requires a global state space analysis that motivates…
In the present paper we have discussed the mechanics of incompressible test bodies moving in Riemannian spaces with non-trivial curvature tensors. For Hamilton's equations of motion the solutions have been obtained in the parametrical form…
We develop a general mapping from given kink or pulse shaped travelling-wave solutions including their velocity to the equations of motion on one-dimensional lattices which support these solutions. We apply this mapping - by definition an…
In this article, we are concerned with the following geometric equation \begin{equation}\label{MainEq} \Delta^2 u = -u^{-q} \qquad \text{in } \mathbf{R}^3 \end{equation} for $q>0$. Recently in \cite{GWZ18}, Guo, Wei and Zhou have…
This paper deals with the equation $-\Delta u+\mu u=f$ on high-dimensional spaces $\mathbb{R}^m$, where the right-hand side $f(x)=F(Tx)$ is composed of a separable function $F$ with an integrable Fourier transform on a space of a dimension…
Traveling waves for the FPU chain are constructed by solving the associated equation for the spatial profile $u$ of the wave. We consider solutions whose derivatives $u'$ need not be small, may change sign several times, but decrease at…
A singularly perturbed free boundary problem arising from a real problem associated with a Radiographic Integrated Test Stand concerns a solution of the equation $\Delta u = f(u)$ in a domain $\Omega$ subject to constant boundary data,…
We investigate integral formulations and fast algorithms for the steady-state radiative transfer equation with isotropic and anisotropic scattering. When the scattering term is a smooth convolution on the unit sphere, a model reduction step…
We consider stationary axisymmetric solutions of the Euler-Poisson equations, which govern the internal structure of barotropic gaseous stars. We take the general form of the equation of states which cover polytropic gaseous stars indexed…
We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an…
In the presence of a chemically active particle, a nearby chemically inert particle can respond to a concentration gradient and move by diffusiophoresis. The nature of the motion is studied for two cases: first, a fixed reactive sphere and…
In this short note, we present an easy to implement and fast algorithm for the computation of the steady solitary gravity wave solution of the free surface Euler equations in irrotational motion. First, the problem is reformulated in a…
We are concerned with the asymptotic behaviour of classical solutions of systems of the form u_t = Au_xx + f(u, u_x), x in R, t>0, u(x,t) a vector in RN, with u(x,0)= U(x), where A is a positive-definite diagonal matrix and f is a…
The modified theories of gravity, especially the f(R) theory, have attracted much attention in recent years. In this context, we explore static plane symmetric vacuum solutions using the metric approach of this theory. The field equations…