16 citations · 41 across the 12 of their papers we have counts for
14 papers
Asymptotics and Scattering for Critically Weakly Hyperbolic and Singular Systems
Bolys Sabitbek, Arick Shao
We study a very general class of first-order linear hyperbolic systems that both become weakly hyperbolic and contain lower-order coefficients that blow up at a single time …
Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, III: singular coefficients
Claudia Garetto, Bolys Sabitbek
In this paper we continue the analysis of non-diagonalisable hyperbolic systems initiated in \cite{GarJRuz, GarJRuz2}. Here we assume that the system has discontinuous coefficients…
Blow-up solutions of damped Klein-Gordon equation on the Heisenberg group
Michael Ruzhansky, Bolys Sabitbek
Inthisnote,weprovetheblow-upofsolutionsofthesemilineardamped Klein-Gordon equation in a finite time for arbitrary positive initial energy on the Heisenberg group. This work complem…
Global existence and nonexistence of semilinear wave equation with a new condition
Bolys Sabitbek
In this paper, we consider the initial-boundary problem for semilinear wave equation with a new condition for some positive constants…
Global existence and blow-up of solutions to porous medium equation and pseudo-parabolic equation, I. Stratified Groups
Michael Ruzhansky, Bolys Sabitbek, Berikbol Torebek
In this paper, we prove a global existence and blow-up of the positive solutions to the initial-boundary value problem of the nonlinear porous medium equation and the nonlinear pse…
Global existence and blow-up of solutions to the double nonlinear porous medium equation
Bolys Sabitbek, Berikbol Torebek
In this study, we examine a double nonlinear porous medium equation subject to a novel nonlinearity condition within a bounded domain. First, we introduce the blow-up solution for…
Hardy and Rellich inequalities with Bessel pairs
Michael Ruzhansky, Bolys Sabitbek
In this paper, we establish suitable characterisations for a pair of functions on a bounded, connected domain in order to have the following H…
Principal frequency of p-sub-Laplacians for general vector fields
Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan
In this paper, we prove the uniqueness and simplicity of the principal frequency (or the first eigenvalue) of the Dirichlet p-sub-Laplacian for general vector fields. As a byproduc…
Geometric Hardy inequalities on starshaped sets
Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan
In this paper, we present the geometric Hardy inequalities on the starshaped sets in the Carnot groups. Also, we obtain the geometric Hardy inequalities on half-spaces for general…
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…
Weighted anisotropic Hardy and Rellich type inequalities for general vector fields
Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan
In this paper, we establish the weighted anisotropic Hardy and Rellich type inequalities with boundary terms for general (real-valued) vector fields. As consequences, we derive new…
Subelliptic geometric Hardy type inequalities on half-spaces and convex domains
Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan
In this paper we present and versions of the geometric Hardy inequalities in half-spaces and convex domains on stratified (Lie) groups. As a consequence, we obtain the…
Hardy and Rellich inequalities for anisotropic p-sub-Laplacians
Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan
In this paper we establish the subelliptic Picone type identities. As consequences, we obtain Hardy and Rellich type inequalities for anisotropic p-sub- Laplacians which are operat…
Weighted -Hardy and -Rellich inequalities with boundary terms on stratified Lie groups
Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan
In this paper, generalised weighted -Hardy,-Caffarelli-Kohn-Nirenberg, and -Rellich inequalities with boundary terms are obtained on stratified Lie groups. As conse…