Related papers: The Stokes phenomenon for certain partial differen…
The swimming of a sphere by means of radial helical surface waves is studied on the basis of the Stokes equations. Explicit expressions are derived for the matrices characterizing the mean translational and rotational swimming velocities…
This paper studies high-order partial differential equations with random initial conditions that have both long-memory and cyclic behavior. The cases of random initial conditions with the spectral singularities, both at zero (representing…
We derive a generalized Stokes' theorem, valid in any dimension and for arbitrary loops, even if self intersecting or knotted. The generalized theorem does not involve an auxiliary surface, but inherits a higher rank gauge symmetry from the…
Consider the stochastic heat equation $\partial_t u = \sL u + \dot{W}$, where $\sL$ is the generator of a [Borel right] Markov process in duality. We show that the solution is locally mutually absolutely continuous with respect to a smooth…
Analysis of the Navier-Stokes equations in the frames of the algebraic approach to systems of partial differential equations (formal theory of differential equations) is presented.
Optical frequency conversion by four-wave mixing (Bragg scattering) in a fiber is considered. The evolution of this process can be modeled using the signal and idler amplitudes, which are complex, or Stokes-like parameters, which are real.…
When we have two expansions of physical quantity around two different points in parameter space, we can usually construct a family of functions, which interpolates the both expansions. In this paper we study analytic structures of such…
We covariantize calculations over the manifold of phase space, establishing Stokes' theorem for differential cross sections and providing new definitions of familiar observable properties like infrared and collinear safety. Through the…
We show that most of the empirical or semi-empirical isotherms proposed to extend the Langmuir formula to sorption (adsorption, chimisorption and biosorption) on heterogeneous surfaces in the gaseous and liquid phase belong to the family…
We show among other things how knowing Schauder or Sobolev-space estimates for the one-dimensional heat equation allows one to derive their multidimensional analogs for equations with coefficients depending only on time variable with the…
We examine the exponentially improved asymptotic expansion of the Lerch zeta function $L(\lambda,a,s)=\sum_{n=1}^\infty \exp (2\pi ni\lambda)/(n+a)^s$ for large complex values of $a$, with $\lambda$ and $s$ regarded as parameters. It is…
We formulate thermodynamics of economic systems in terms of an arbitrary probability distribution for a conserved economic quantity. As in statistical physics, thermodynamic macroeconomic variables emerge as the mean value of microeconomic…
Rapid processes of heat transfer are not described by the standard heat conduction equation. To take into account a finite velocity of heat transfer, we use the hyperbolic model of heat conduction, which is connected with the relaxation of…
This article is devoted to the analysis of inverse source problems for Stokes systems in unbounded domains where the corresponding velocity flow is observed on a surface. Our main objective is to study the unique determination of general…
A rigorous way to obtain sharp bounds for Stokes constants is introduced and illustrated on a concrete problem arising in applications.
We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…
We generalize Gassert-Shor formula for numerical semigroups.
We prove that formal WKB solutions of Schr\"odinger equations on Riemann surfaces are resurgent. Specifically, they are Borel summable in almost all directions and their Borel transforms admit endless analytic continuation away from a…
We study the strong solvability of the nonstationary Stokes problem with non-zero divergence in a bounded domain.
In this paper, we consider a q-analogue of the Borel-Laplace summation where q>1 is a real parameter. In particular, we show that the Borel-Laplace summation of a divergent power series solution of a linear differential equation can be…