Related papers: A non-increasing Lindley-type equation

This paper studies the asymptotic behaviour of the solution of a differential equation perturbed by a fast flow preserving an infinite measure. This question is related with limit theorems for non-stationary Birkhoff integrals. We…

We study the elliptic inclusion given in the following divergence form \begin{align*} & -\mathrm{div}\, A(x,\nabla u) \ni f\quad \mathrm{in}\quad \Omega, & u=0\quad \mathrm{on}\quad \partial \Omega. \end{align*} As we assume that $f\in…

In this paper, we study the regularity of solutions to a linear elliptic equation involving a mixed local-nonlocal operator of the form $$Lu - \operatorname{div}\big(a(x)\nabla u(x)\big)= f, \quad \text{in } \Omega \subset \mathbb{R}^n,$$…

For the basic maximum likelihood estimating function of the two parameters Weibull distribution, a simple proof on its global monotonicity is given to ensure the existence and uniqueness of its solution. The boundary of the function's…

A nonlinear Schrodinger equation arising from light propagation down an inhomogeneous medium is considered. The inhomogeneity is reflected through a non-uniform coefficient of the non-linear term in the equation. In particular, a…

We explore the Wilks phenomena in two random graph models: the $\beta$-model and the Bradley-Terry model. For two increasing dimensional null hypotheses, including a specified null $H_0: \beta_i=\beta_i^0$ for $i=1,\ldots, r$ and a…

We study the equations obtained from linearizing the compressible Navier-Stokes equations around a steady-state profile with a heavier fluid lying above a lighter fluid along a planar interface, i.e. a Rayleigh-Taylor instability. We…

We prove existence of renormalized solutions to general nonlinear elliptic equation in Musielak-Orlicz space avoiding growth restrictions. Namely, we consider \begin{equation*} -{\rm div} A(x,\nabla u)= f\in L^1(\Omega), \end{equation*} on…

In this paper we consider the distribution of the maximum of a Gaussian field defined on non locally convex sets. Adler and Taylor or Aza\"\i s and Wschebor give the expansions in the locally convex case. The present paper generalizes their…

We deal with nonlinear weighted biharmonic problem in the unit ball of $\mathbb{R}^{4}$. The weight is of logarithm type. The nonlinearity is critical in view of Adam's inequalities in the weighted Sobolev space $W^{2,2}_{0}(B,w)$. We prove…

A tube conveying a large amount of fluid with a free outlet does not sit still. We construct and analyze a nonlinear evolution equation describing such phenomena. Two types of boundary conditions at the inlet are considered, one for which…

We investigate the nonlinear instability of a smooth Rayleigh-Taylor steady-state solution (including the case of heavier density with increasing height) to the three-dimensional incompressible nonhomogeneous magnetohydrodynamic (MHD)…

In the paper we study a measure version of the evolutionary nonlinear Boltzmann-type equation in which we admit a random number of collisions of particles. We consider first a stationary model and use two methods to find its fixed points:…

We consider the evolutionary Hamilton-Jacobi equation \begin{align*} w_t(x,t)+H(x,Dw(x,t),w(x,t))=0, \quad(x,t)\in M\times [0,+\infty), \end{align*} where $M$ is a compact manifold, $H:T^*M\times R\to R$, $H=H(x,p,u)$ satisfies Tonelli…

A second order accurate numerical scheme is proposed and implemented for the Landau-Lifshitz-Gilbert equation, which models magnetization dynamics in ferromagnetic materials, with large damping parameters. The main advantages of this method…

Variational problems of splitting-type with mixed linear-superlinear growth conditions are considered. In the twodimensional case the minimizing problem is given by \[ J [w] = \int_{\Omega} \Big[f_1\big(\partial_1 w\big) +…

In this paper we prove a Liouville type theorem for the stationary equations of a non-Newtonian fluid in $\mathbb{R}^3$ with the viscous part of the stress tensor $\mathbf{A}_p(u) = \mathrm{div} ( | \mathbf{D}(u) |^{p-2} \mathbf{D}(u) )$,…

A nonlinear extension of Schr\"odinger's wave equation is proposed that ensures non-signaling by keeping linear the evolution of \textit{coordinate-diagonal} elements of the density matrix. The equation contains a negative kinetic energy…

In this paper, we consider the problem of nonlinear (in particular, saturated) stabilization of the high-dimensional wave equation with Dirichlet boundary conditions. The wave dynamics are subject to a dissipative nonlinear velocity…

We address the problem of constructing a non-equilibrium stationary state for a one-dimensional stochastic Klein-Gordon wave equation with non-linearity, using perturbation theory. The linear theory is reviewed, but with the linear…