相关论文: Asymptotic expansion of planar canard solutions ne…

Compaction in reactive porous media is modelled as a reaction-diffusion process with a moving boundary. Asymptotic analysis is used to find solutions for the coupled nonlinear compaction equations, and a traveling wave solution is obtained…

We construct an asymptotic expansion in powers of the coupling constant directly of the cross-section for pair production and decay of fundamental unstable particles. The resonant and kinematic singularities arising in the expansion we…

In this paper, we study phase transitions in a slender circular cylinder composed of a compressible hyperelastic material with a non-convex strain energy function. We aim to construct the asymptotic solutions based on an axisymmetrical…

In a growth-fragmentation system, cells grow in size slowly and split apart at random. Typically, the number of cells in the system grows exponentially and the distribution of the sizes of cells settles into an equilibrium 'asymptotic…

We calculate asymptotic expansions for the moments of number of comparisons used by the randomized quick sort algorithm using the singularity analysis of certain generating functions.

We study the nodal intersections number of random Gaussian toral Laplace eigenfunctions ("arithmetic random waves") against a fixed smooth reference curve. The expected intersection number is proportional to the the square root of the…

We find convergent double series expansions for Legendre's third incomplete elliptic integral valid in overlapping subdomains of the unit square. Truncated expansions provide asymptotic approximations in the neighbourhood of the logarithmic…

The asymptotic analysis of Bergman kernels with respect to exponentially varying measures near emergent interfaces has attracted recent attention. Such interfaces typically occur when the associated limiting Bergman density function…

For a family of second-order parabolic systems with rapidly oscillating and time-dependent periodic coefficients, we investigate the asymptotic behavior of fundamental solutions and establish sharp estimates for the remainders.

The problem of parameter estimation by observations of inhomogeneous Poisson processes is considered. The method of moments estimator is studied and its stochastic expansion is obtained. This stochastic expansion is then used to obtain the…

In this paper, it is shown that the solutions of general differentiable constrained optimization problems can be viewed as asymptotic solutions to sets of Ordinary Differential Equations (ODEs). The construction of the ODE associated to the…

Is studied asymptotic expansion for solution of singularly perturbed equation for functional of Markovian evolution in Rd. The view of regular and singular parts of solution is found.

The aim of this paper is investigating the existence of solutions of some semilinear elliptic problems on open bounded domains when the nonlinearity is subcritical and asymptotically linear at infinity and there is a perturbation term which…

We provide a rigorous derivation of an asymptotic formula for perturbations in the resonance values caused by the presence of finite number of anisotropic imperfections of small shapes with constitutive parameters different from the…

We study the asymptotic limit of the Cahn-Hilliard equation on an evolving surface with prescribed velocity. The method of formally matched asymptotic expansions is extended to account for the movement of the domain. We consider various…

The exponential family of random graphs has been a topic of continued research interest. Despite the relative simplicity, these models capture a variety of interesting features displayed by large-scale networks and allow us to better…

Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, valuable insights can be gained through their asymptotic…

We study the asymptotic behavior of a diffusion process with small diffusion in a domain $D$. This process is reflected at $\partial D$ with respect to a co-normal direction pointing inside $D$. Our asymptotic result is used to study the…

We study some asymptotic properties of cylinder processes in the plane defined as union sets of dilated straight lines (appearing as mutually overlapping infinitely long strips) derived from a stationary independently marked point process…

We study the defocusing nonlinear Schr\"odinger equation in the quarter plane with asymptotically periodic boundary values. By studying an associated Riemann-Hilbert problem and employing nonlinear steepest descent arguments, we construct…