Related papers: The Kramers problem for Holway-Shakhov equation
We show how pairs of isothermic surfaces are given by curved flats in a pseudo Riemannian symmetric space and vice versa. Calapso's fourth order partial differential equation is derived and, using a solution of this equation, a M\"obius…
We investigate the Smoluchowski-Kramers approximation for the one-dimensional periodic variational wave equation with state-dependent damping and additive noise. We show that weak ``dissipative'' solutions converge to solutions of a…
A solution of the Riemann problem is constructed for a nonstrictly hyperbolic inhomogeneous system of equations describing one-dimensional cold plasma oscillations. Each oscillation period includes one rarefaction wave and one shock wave…
The relationship between short and long time relaxation dynamics is obtained for a simple solvable two-level energy landscape model of a glass. This is done through means of the Kramers transition theory, which arises in very natural manner…
According to the Smoluchowski-Kramers approximation, the solution of the equation ${\mu}\ddot{q}^{\mu}_t=b(q^{\mu}_t)-\dot{q}^{\mu}_t+{\Sigma}(q^{\mu}_t)\dot{W}_t, q^{\mu}_0=q, \dot{q}^{\mu}_0=p$ converges to the solution of the equation…
The experiment shows that small liquid droplets under the action of gravity and the Archimedes force move in the external viscous liquid practically according to the Stokes drag force equation, and not in accordance with the…
A simple algorithm for the inverse scattering approach to the Camassa-Holm equation is presented.
We use the Chapman-Enskog method to derive the Smoluchowski equation from the Kramers equation in a high friction limit. We consider two main extensions of this problem: we take into account a uniform rotation of the background medium and…
We provide a new, concise proof of weak existence and uniqueness of solutions to the stochastic differential equation for the multidimensional skew Brownian motion. We also present an application to Brownian particles with skew-elastic…
In this paper we consider the problem of analytical continuation of solutions to the system of thermoelasticity in a bounded domain from their values and values of their strains on a part of the boundary of this domain, i.e., the Cauchy…
The heat equation is often used in order to inpaint dropped data in inpainting-based lossy compression schemes. We propose an alternative way to numerically solve the heat equation by an extended Krylov subspace method. The method is very…
We obtain necessary conditions and sufficient conditions on the existence of solutions to the Cauchy problem for a fractional semilinear heat equation with an inhomogeneous term. We identify the strongest spatial singularity of the…
Thermodynamics of extended gravity static spherically symmetric black hole solutions is investigated. The energy issue is discussed making use of the derivation of Clausius relation from equations of motion, evaluating the black hole…
New inverse and half-inverse problems: {\it sliding problems} are introduced. In this way several physically important equations are recovered from the quantum defect. In particular, sliding problems are solved for radial Schr\"odinger…
A mathematical model allowing coupled hygro-thermo-mechanical analysis of spalling in concrete walls at high temperatures by means of the moving boundary problem is presented. A simplified mechanical approach to account for effects of…
The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle…
Hamilton's equations with noise and friction possess a hidden supersymmetry, valid for time-independent as well as periodically time-dependent systems. It is used to derive topological properties of critical points and periodic trajectories…
We establish the existence of smooth critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds for smooth convex Hamiltonians, that is in the context of weak KAM theory, under the assumption that the Aubry set is the union…
The Kelvin problem of an isotropic elastic space subject to a concentrated load is solved in a manner that exploits the problem's built-in symmetries so as to determine in the first place the unique balanced and compatible stress field.
When a solution to an abstract inverse linear problem on Hilbert space is approximable by finite linear combinations of vectors from the cyclic subspace associated with the datum and with the linear operator of the problem, the solution is…