On the singular behavior of solutions of a transmission problem in a dihedral.
On the singular limit in a phase field model of phase transitions
On the singular limit of solutions to the Cox-Ingersoll-Ross interest rate model with stochastic volatility
In this paper we are interested in term structure models for pricing zero coupon bonds under rapidly oscillating stochastic volatility. We analyze solutions to the generalized Cox–Ingersoll–Ross two factors model describing clustering of interest rate volatilities. The main goal is to derive an asymptotic expansion of the bond price with respect to a singular parameter representing the fast scale for the stochastic volatility process. We derive the second order asymptotic expansion of a solution...
On the Singularities of the Solution to the Cauchy Problem with Singular Data in the Complex Domain.
On the smoothness of solutions of variational inequalities with obstacles
On the solutions of Knizhnik-Zamolodchikov system
We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions. We prove that under some conditions the solution of the KZ system is rational too. We give the method of constructing the corresponding rational solution. We deduce the asymptotic formulas for the solution of the KZ system when the parameter ρ is an integer.
On the solutions of nonlinear initial-boundary value problems.
On the solvability of a class of singular parabolic equations with nonlocal boundary conditions in nonclassical function spaces.
On the solvability of a nonlocal problem arising in dynamics of moisture transfer.
On the solvability of a system of wave and beam equations.
On the solvability of nonlocal pluriparabolic problems.
On the solvability of parabolic and hyperbolic problems with a boundary integral condition.
On the Solvability of Semilinear Elliptic Equations with Nonlinear Boundary Conditions.
On the spatial analyticity of solutions to the Keller-Segel equations
The regularizing rate of solutions to the Keller-Segel equations in the whole space is estimated just as for the heat equation. As an application of these rate estimates, it is proved that the solution is analytic in spatial variables. Spatial analyticity implies that the propagation speed is infinite, i.e., the support of the solution coincides with the whole space for any short time, even if the support of the initial datum is compact.
On the stability of solitary waves for classical scalar fields
On the stability of solutions of impulsive nonlinear parabolic equations
On the stability of solutions of impulsive nonlinear parabolic equations
Stability and asymptotic stability of the solutions of impulsive nonlinear pa ra bo lic equations are studied via the method of differential inequalities.
On the stability of solutions of nonlinear parabolic differential-functional equations
We consider a nonlinear differential-functional parabolic boundary initial value problem (1) ⎧A z + f(x,z(t,x),z(t,·)) - ∂z/∂t = 0 for t > 0, x ∈ G, ⎨z(t,x) = h(x) for t > 0, x ∈ ∂G, ⎩z(0,x) = φ₀(x) for x ∈ G, and the associated elliptic boundary value problem with Dirichlet condition (2) ⎧Az + f(x,z(x),z(·)) = 0 for x ∈ G, ⎨z(x) = h(x) for x ∈ ∂G ⎩ where , G is an open and bounded domain with (0 < α ≤ 1) boundary, the operator Az := ∑j,k=1m ajk(x) (∂²z/(∂xj ∂xk)) is...
On the stability of the Dirichlet problem for the vibrating string equation
On the stabilization of laminated beams with delay
Of concern in this paper is the laminated beam system with frictional damping and an internal constant delay term in the transverse displacement. Under suitable assumptions on the weight of the delay, we establish that the system's energy decays exponentially in the case of equal wave speeds of propagation, and polynomially in the case of non-equal wave speeds.