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20 papers · 2 filters
Optimal extinction rates for the fast diffusion equation with strong absorption
Razvan Iagar, Philippe Laurençot
Optimal extinction rates near the extinction time are derived for non-negative solutions to a fast diffusion equation with strong absorption, the power of the absorption exceeding…
On a stochastic Hardy-Littlewood-Sobolev inequality with application to Strichartz estimates for the white noise dispersion
Romain Duboscq, Anthony Réveillac
In this paper, we investigate a stochastic Hardy-Littlewood-Sobolev inequality. Due to the stochastic nature of the inequality, the relation between the exponents of intgrability i…
On the Heston Model with Stochastic Volatility: Analytic Solutions and Complete Markets
Bénédicte Alziary, Peter Takáč
We study the Heston model for pricing European options on stocks with stochastic volatility. This is a Black\--Scholes\--type equation whose spatial domain for the logarithmic stoc…
Blowup of solutions for a class of the focusing inhomogeneous nonlinear Schrödinger equation
Van Duong Dinh
In this paper, we consider a class of the focusing inhomogeneous nonlinear Schrödinger equation \[ i\partial_t u + Δu + |x|^{-b} |u|^αu = 0, \quad u(0)=u_0 \in H^1(\mathbb{R}^d), \…
Energy scattering for a class of the defocusing inhomogeneous nonlinear Schrödinger equation
Van Duong Dinh
In this paper, we consider a class of the defocusing inhomogeneous nonlinear Schrödinger equation \[ i\partial_t u + Δu - |x|^{-b} |u|^αu = 0, \quad u(0)=u_0 \in H^1, \] with $b, α…
Spherical particle in a nematic liquid crystal under an external field: the Saturn ring regime
Stan Alama, Lia Bronsard, Xavier Lamy
We consider a nematic liquid crystal occupying the exterior region in R^3 outside of a spherical particle, with radial strong anchoring. Within the context of the Landau-de Gennes…