Second-order boundary estimates for solutions to singular elliptic equations in borderline cases.
Second-order boundary estimates for solutions to singular elliptic equations.
Second-order estimates for boundary blowup solutions of special elliptic equations.
Selfadjoint Extensions for the Elasticity System in Shape Optimization
Two approaches are proposed to modelling of topological variations in elastic solids. The first approach is based on the theory of selfadjoint extensions of differential operators. In the second approach function spaces with separated asymptotics and point asymptotic conditions are introduced, and a variational formulation is established. For both approaches, accuracy estimates are derived.
Self-similar singular solution of doubly singular parabolic equation with gradient absorption term.
Self-similar solutions for the two-dimensional Nernst-Planck-Debye system
We investigate the two-component Nernst-Planck-Debye system by a numerical study of self-similar solutions using the Runge-Kutta method of order four and comparing the results obtained with the solutions of a one-component system. Properties of the solutions indicated by numerical simulations are proved and an existence result is established based on comparison arguments for singular ordinary differential equations.
Semiclassical fundamental solutions.
Series solutions of time-fractional PDEs by homotopy analysis method.
Sheaves on subanalytic sites
Short-time Asymptotics of the two-Dimensional wave Equation for an Annular Vibrating Membrane with Piecewise smooth Boundary Conditions
Single-point blow-up on the boundary where the zero Dirichlet boundary condition is imposed
We consider a reaction-diffusion-convection equation on the halfline (0,1) with the zero Dirichlet boundary condition at . We find a positive selfsimilar solution which blows up in a finite time at while remains bounded for .
Singular solutions of the Briot-Bouquet type partial differential equations
Singularités d'arêtes pour les problèmes aux limites elliptiques
Solitary wave and other solutions for nonlinear heat equations
A number of explicit solutions for the heat equation with a polynomial non-linearity and for the Fisher equation is presented. An extended class of non-linear heat equations admitting solitary wave solutions is described. The generalization of the Fisher equation is proposed whose solutions propagate with arbitrary ad hoc fixed velocity.
Solitary wave solutions for a time-fraction generalized Hirota-Satsuma coupled KdV equation by a new analytical technique.
Solitary waves for a coupled nonlinear Schrödinger system with dispersion management.
Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise.
Solitons and Gibbs Measures for Nonlinear Schrödinger Equations
We review some recent results concerning Gibbs measures for nonlinear Schrödinger equations (NLS), with implications for the theory of the NLS, including stability and typicality of solitary wave structures. In particular, we discuss the Gibbs measures of the discrete NLS in three dimensions, where there is a striking phase transition to soliton-like behavior.
Solution explicite du problème de Cauchy pour un opérateur hyperbolique à caractéristiques non régulières
Solution of a spectral problem for the curl operator on a cylinder.