11 papers
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 irregular coefficients. We first establish clas…
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…
Nonlinear Dirac equations on noncompact quantum graphs with potentials: Multiplicity and Concentration
Guangze Gu, Ziwei Li, Michael Ruzhansky +1
In this paper, we study the existence and multiplicity of solutions to the following class of nonlinear Dirac equations (NLDE) on noncompact quantum graphs: \[ -i\,\varepsilon c\,Ï…
Numerical Approaches for Identifying the Time-Dependent Potential Coefficient in the Diffusion Equation
Arshyn Altybay, Michael Ruzhansky
We address the inverse problem of identifying a time-dependent potential coefficient in a one-dimensional diffusion equation subject to Dirichlet boundary conditions and a nonlocal…