5 papers · 1 filter
On a fractional nonlinear Schrödinger equation with irregular coefficients. case: d<2s
Arshyn Altyby, Michael Ruzhansky, Mohammed Elamine Sebih +1
In the case when , where is the space dimension and is the fractional power of the Laplacian, we study the well-posedness for a cubic nonlinear Schrödinger equation…
Functional calculus for Safarov pseudo-differential operators
Santiago Gómez Cobos, Michael Ruzhansky
Given a smooth, closed Riemannian manifold equipped with a linear connection (not necessarily metric), we develop the holomorphic functional calculus for operators…
Parabolic equations with concave non-linearity
Zhirayr Avetisyan, Khachatur Khachatryan, Michael Ruzhansky
In this paper we prove the existence and uniqueness of positive mild solutions for the semilinear parabolic equations of the form , where is a p…
Fractional Hardy type inequalities on homogeneous Lie groups in the case
Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan
In this paper, we obtain a fractional Hardy inequality in the case on homogeneous Lie groups, and as an application we show the corresponding uncertainty principle. Also, we…
Integro-differential diffusion equations on graded Lie groups
Joel E. Restrepo, Michael Ruzhansky, Berikbol T. Torebek
We first study the existence, uniqueness and well-posedness of a general class of integro-differential diffusion equation on , is a gra…