115 citations · 1.9k across the 226 of their papers we have counts for
13 papers · 2 filters
Inverse source problems for positive operators. I. Hypoelliptic diffusion and subdiffusion equations
Michael Ruzhansky, Niyaz Tokmagambetov, Berikbol T. Torebek
A class of inverse problems for restoring the right-hand side of a parabolic equation for a large class of positive operators with discrete spectrum is considered. The results on e…
Existence and non-existence of global solutions for semilinear heat equations and inequalities on sub-Riemannian manifolds, and Fujita exponent on unimodular Lie groups
Michael Ruzhansky, Nurgissa Yessirkegenov
In this paper we study the global well-posedness of the following Cauchy problem on a sub-Riemannian manifold : \begin{equation*} \begin{cases} u_{t}-\mathfrak{L}_{M} u=f(u), \;…
On a non-local problem for a multi-term fractional diffusion-wave equation
Michael Ruzhansky, Niyaz Tokmagambetov, Berikbol T. Torebek
This paper deals with the multi-term generalisation of the time-fractional diffusion-wave equation for general operators with discrete spectrum, as well as for positive hypoellipti…
Geometric Hardy and Hardy-Sobolev inequalities on Heisenberg groups
Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan
In this paper, we present the geometric Hardy inequality for the sub-Laplacian in the half-spaces on the stratified groups. As a consequence, we obtain the following geometric Hard…
On a class of anharmonic oscillators
Marianna Chatzakou, Julio Delgado, Michael Ruzhansky
In this work we study a class of anharmonic oscillators within the framework of the Weyl-Hörmander calculus. The anharmonic oscillators arise from several applications in mathemati…
Very weak solutions to hypoelliptic wave equations
Michael Ruzhansky, Nurgissa Yessirkegenov
In this paper we study the Cauchy problem for the wave equations for hypoelliptic homogeneous left-invariant operators on graded Lie groups when the time-dependent non-negative pro…