Related papers: Multiscale Gevrey asymptotics in boundary layer ex…

We provide fine asymptotics of solutions of fractional elliptic equations at boundary points where the domain is locally conical; that is, corner type singularities appear. Our method relies on a suitable smoothing of the corner singularity…

This article studies a dirichlet boundary value problem for singularly perturbed time delay convection diffusion equation with degenerate coefficient. A priori explicit bounds are established on the solution and its derivatives. For…

Consider neutron transport equations in 3D convex domains with in-flow boundary. We mainly study the asymptotic limits as the Knudsen number $\epsilon\rightarrow 0^+$. Using Hilbert expansion, we rigorously justify that the solution of…

We prove the existence of a 1/N expansion in unitary multimatrix models which are Gibbs perturbations of the Haar measure, and express the expansion coefficients recursively in terms of the unique solution of a noncommutative initial value…

We propose a geometric approach for the numerical integration of singular initial value problems for (systems of) quasi-linear differential equations. It transforms the original problem into the problem of computing the unstable manifold at…

Recently, the present authors derived new asymptotic expansions for linear differential equations having a simple turning point. These involve Airy functions and slowly varying coefficient functions, and were simpler than previous…

A class of quasilinear singularly perturbed boundary value problems with a turning point of attractive type is considered. The problems are solved numerically by a finite-difference scheme on a special discretization mesh which is dense…

We study a two-point free boundary problem in a sector for a quasilinear parabolic equation. The boundary conditions are assumed to be spatially and temporally "self-similar" in a special way. We prove the existence, uniqueness and…

Lie symmetry method is applied to find analytic solutions of initial-boundary-value problems of transient conduction in semi-infinite solid with constant surface temperature or constant heat flux condition. The solutions are obtained in a…

For open radial sets $\Omega\subset \mathbb{R}^N$, $N\geq 2$ we consider the nonlinear problem \[ (P)\quad Iu=f(|x|,u) \quad\text{in $\Omega$,}\quad u\equiv 0\quad \text{on $\mathbb{R}^N\setminus \Omega$ and }\lim_{|x|\to\infty} u(x)=0, \]…

We exploit an arbitrary extrinsic time foliation of spacetime to solve the constraints in spherically symmetric general relativity. Among such foliations there is a one parameter family, linear and homogeneous in the extrinsic curvature,…

There is scientific and industrial interest in understanding how geologic faults respond to transient sources of fluid. Natural and artificial sources can elevate pore fluid pressure on the fault frictional interface, which may induce slip.…

A class of different schemes for the numerical solving of semilinear singularly--perturbed reaction--diffusion boundary--value problems was constructed. The stability of the difference schemes was proved, and the existence and uniqueness of…

We consider the size of the nodal set of the solution of the second order parabolic-type equation with Gevrey regular coefficients. We provide an upper bound as a function of time. The dependence agrees with a sharp upper bound when the…

This work investigates a nonlocal sinh-Gordon equation with a singularly perturbed parameter in a ball. Under the Robin boundary condition, the solution asymptotically forms a quite steep boundary layer in a thin annular region, and rapidly…

We consider a semi-linear parabolic problem in a model plane thick fractal junction $\Omega_{\varepsilon}$, which is the union of a domain $\Omega_{0}$ and a lot of joined thin trees situated $\varepsilon$-periodically along some interval…

We consider time-inhomogeneous ODEs whose parameters are governed by an underlying ergodic Markov process. When this underlying process is accelerated by a factor $\varepsilon^{-1}$, an averaging phenomenon occurs and the solution of the…

To explain the phenomenon of bifurcation delay, which occurs in planar systems of the form $\dot{x}=\epsilon f(x,z,\epsilon)$, $\dot{z}=g(x,z,\epsilon)z$, where $f(x,0,0)>0$ and $g(x,0,0)$ changes sign at least once on the $x$-axis, we use…

The existence of numerical solutions to a fourth order singular boundary value problem arising in the theory of epitaxial growth is studied. An iterative numerical method is applied on a second order nonlinear singular boundary value…

Evolution PDEs for dispersive waves are considered in both linear and nonlinear integrable cases, and initial-boundary value problems associated with them are formulated in spectral space. A method of solution is presented, which is based…