2 citations · 3 across the 16 of their papers we have counts for
15 papers · 1 filter
Topological Effects on Bubbling in the Critical Dirichlet Problem on Hyperbolic Domains:
Tapendu Rana, Michael Ruzhansky, Zhipeng Yang
Let \(Ω\Subset\mathbb H^N\), \(N\in\{3,4,5\}\), be a bounded connected \(C^2\) domain. We prove that the pure critical Dirichlet problem \[ -Δ_{\mathbb H}u=u^{\frac{N+2}{N-2}} \qua…
Very weak solutions of the heat equation with anisotropically singular time-dependent diffusivity
Zhirayr Avetisyan, Zahra Keyshams, Monire Mikaeili Nia +1
We investigate the heat equation with a time-dependent, anisotropic, and potentially singular diffusivity tensor. Since weak (in the Sobolev sense) or distributional solutions may…
Heat Equation driven by mixed local-nonlocal operators with non-regular space-dependent coefficients
Arshyn Altybay, Michael Ruzhansky
In this paper, we study the Cauchy problem for a heat equation governed by a mixed local--nonlocal diffusion operator with spatially dependent coefficients. For bounded measurable…
Normalized Solutions and Semiclassical Concentration for Upper-Critical Fractional Choquard Equations
Yergen Aikyn, Yongpeng Chen, Michael Ruzhansky +1
We study a fractional Choquard equation with an upper-critical Hartree term, an -supercritical Hartree perturbation, and a semiclassical potential under a prescribed -mas…
Multiplicity of bound states for a class of nonlinear Dirac equations on generalized star graphs with potentials
Guangze Gu, Ziwei Li, Michael Ruzhansky +1
In this paper we investigate the existence and multiplicity of bound states for a class of nonlinear Dirac equations on a generalized star graph \(\mathcal{G}\): \[ -ic\,σ_1\,\part…
Nonrelativistic limit of bound-state solutions for nonlinear Dirac equation on noncompact quantum graphs
Guangze Gu, Michael Ruzhansky, Guoyan Wei +1
In this paper, we investigate the nonrelativistic limit and qualitative properties of bound-state solutions for the nonlinear Dirac equation (NLDE) defined on noncompact quantum gr…
Very weak solutions of the heat equation with anisotropically singular time-dependent diffusivity
Zhirayr Avetisyan, Zahra Keyshams, Monire Mikaeili Nia +1
We investigate the heat equation with a time-dependent, anisotropic, and potentially singular diffusivity tensor. Since weak (in the Sobolev sense) or distributional solutions may…
Singular Klein-Gordon equation on a bounded domain
Michael Ruzhansky, Alibek Yeskermessuly
In this paper, we consider the wave equation for the Laplace operator with potential, initial data, and nonhomogeneous Dirichlet boundary condition. We establish a weak solution by…
Cylindrical extensions of critical Sobolev type inequalities and identities
Michael Ruzhansky, Yerkin Shaimerdenov, Nurgissa Yessirkegenov
In this paper, we investigate cylindrical extensions of critical Sobolev type (improved Hardy) inequalities and identities in the style of Badiale-Tarantello [BT02], which in a spe…
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…
Boundary value problem for the time-fractional telegraph equation with Caputo derivatives
M. O. Mamchuev
In this paper the Green formula for the operator of fractional differentiation in Caputo sense is proved. By using this formula the integral representation of all regular in a rect…