We study the inverse problem on identifying two unknown potential coefficients in a system of coupled Schrödinger equations in a bounded domain in $\mathbb{R}^{n}$ subject to non - homogeneous Dirichlet and Neumann boundary conditions by using Neumann and Dirichlet boundary measurements. Under specific convexity assumptions on the geometry of domain and minimal regularity conditions on the data, we establish the Lipschitz stability of this inverse problem by employing uniqueness results as well as the observability inequality.
This paper presents a mathematical analysis of the inverse problem concerning the recovery of two unknown potential coefficients in a coupled Schrödinger equations system, within a bounded domain of the Euclidean space Rn with Dirichlet boundary conditions. Our analysis relies on Neumann boundary measurements, where we...
In this article, we prove boundary observability estimates for wave equations on bounded domains $\Omega \subseteq \mathbb{R}^n$, with a critically singular potential that diverges as the inverse square distance to $\partial \Omega$. The result is applicable in all dimensions and for wave equations with general time-de...
This paper investigates the fractional Laplacian equation in half-spaces, focusing on cases with nonlocal Neumann boundary conditions. We consider both single equations and systems, and establish two key principles: the decay at infinity principle and the narrow region principle. These foundational results, combined wi...
We consider a inverse problem for a hyperbolic equation. The objective is to simultaneous recover both the spatially varying coefficient, whose square root represents the wave speed, and the initial displacement from a single pair of Dirichlet-Neumann Cauchy data. By introducing a suitable transformation and differenti...
The aim of this work is to develop a self-contained existence and uniqueness theory for a doubly nonlinear parabolic problem with variable exponents and homogeneous Neumann boundary conditions. Our approach is based on Rothe's time-discretization method and builds on the results established by the author in a previous...
In this manuscript, we study the solvability of a class of mixed-order nabla fractional equations coupled with Dirichlet conditions. Based on the obtained Green’s function and its properties, we establish existence, nonexistence, and multiplicity results using fixed point theory. In the end, we give some numerical exam...
Nikolay D. Dimitrov, J. Jonnalagadda· Fractal and Fractional· 0 citations
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