Stable multiple-layer stationary solutions of a semilinear parabolic equation in two-dimensional domains.
Stable subharmonic solutions and asymptotic behavior in reaction-diffusion equations.
Stacionární teplotní pole v nekonečném válci při součiniteli přestupu tepla periodicky proměnném podél obvodu
Stark stetige Halbgruppen und Gruppen als Lösungen von Cauchy-Problemen in der Mathematischen Physik.
Starke Lösungen semilinearer parabolischer Differentialgleichungen.
State trajectories analysis for a class of tubular reactor nonlinear nonautonomous models.
Stationary solutions, blow up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions.
Steady state temperatures in a quarter plane.
Steady states for a fragmentation equation with size diffusion
The existence of a one-parameter family of stationary solutions to a fragmentation equation with size diffusion is established. The proof combines a fixed point argument and compactness techniques.
Stefan problem in a 2D case
The aim of this paper is to analyze the well posedness of the one-phase quasi-stationary Stefan problem with the Gibbs-Thomson correction in a two-dimensional domain which is a perturbation of the half plane. We show the existence of a unique regular solution for an arbitrary time interval, under suitable smallness assumptions on initial data. The existence is shown in the Besov-Slobodetskiĭ class with sharp regularity in the L₂-framework.
Stochastic calculus and degenerate boundary value problems
Consider the boundary value problem (L.P): in , on where is written as , and is a general Venttsel’s condition (including the oblique derivative condition). We prove existence, uniqueness and smoothness of the solution of (L.P) under the Hörmander’s condition on the Lie brackets of the vector fields (), for regular open sets with a non-characteristic boundary.Our study lies on the stochastic representation of and uses the stochastic calculus of variations for the -diffusion process...
Stochastic FitzHugh-Nagumo equations on networks with impulsive noise.
Stochastic heat equation with white-noise drift
Stochastic reaction diffusion equations and interacting particle systems
Stochastic representation of reflecting diffusions corresponding to divergence form operators
We obtain a stochastic representation of a diffusion corresponding to a uniformly elliptic divergence form operator with co-normal reflection at the boundary of a bounded -domain. We also show that the diffusion is a Dirichlet process for each starting point inside the domain.
Stochastic representations of derivatives of solutions of one-dimensional parabolic variational inequalities with Neumann boundary conditions
In this paper we explicit the derivative of the flows of one-dimensional reflected diffusion processes. We then get stochastic representations for derivatives of viscosity solutions of one-dimensional semilinear parabolic partial differential equations and parabolic variational inequalities with Neumann boundary conditions.
Stochastic Taylor expansions and heat kernel asymptotics
These notes focus on the applications of the stochastic Taylor expansion of solutions of stochastic differential equations to the study of heat kernels in small times. As an illustration of these methods we provide a new heat kernel proof of the Chern–Gauss–Bonnet theorem.
Straightening of a noncylindrical region and evolution equations
Strangely sweeping one-dimensional diffusion
Let X(t) be a diffusion process satisfying the stochastic differential equation dX(t) = a(X(t))dW(t) + b(X(t))dt. We analyse the asymptotic behaviour of p(t) = ProbX(t) ≥ 0 as t → ∞ and construct an equation such that and .
Strong maximum and minimum principles for parabolic functional-differential problems with initial inequalities