2 citations · 3 across the 16 of their papers we have counts for
5 papers · 2 filters
Wave equations for the fractional Sturm-Liouville operator with singular coefficients
Michael Ruzhansky, Mohammed Elamine Sebih, Alibek Yeskermessuly
In this paper, we consider the wave equation for the fractional Sturm-Liouville operator with lower order terms and singular coefficients and data. We prove that the problem has a…
Fractional wave equation with irregular mass and dissipation
Michael Ruzhansky, Mohammed Elamine Sebih, Niyaz Tokmagambetov
In this paper, we pursue our series of papers aiming to show the applicability of the concept of very weak solutions. We consider a wave model with irregular position dependent mas…
Logarithmic Sobolev, Hardy and Poincaré inequalities on the Heisenberg group
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this paper we first prove a number of important inequalities with explicit constants in the setting of the Heisenberg group. This includes the fractional and integer Sobolev, Ga…
Schrödinger equation for Sturm-Liouville operator with singular propagation and potential
M. Ruzhansky, A. Yeskermessuly
In this paper we consider an initial/boundary value problem for the Schrödinger equation with a right-hand side involving the fractional Sturm-Liouville operator with singular prop…
Heat equation for Sturm-Liouville operator with singular propagation and potential
Michael Ruzhansky, Alibek Yeskermessuly
This article considers the initial boundary value problem for the heat equation with the time-dependent Sturm-Liouville operator with singular potentials. To obtain a solution by t…