About

Lorena Bociu is a Professor and Associate Department Head in the Department of Mathematics at NC State University. She earned her PhD from the University of Virginia in 2008. Her expertise lies in the analysis and control of partial differential equations, with applications in nonlinear wave equations, fluid-structure interactions, fluid-solid mixtures, and multiscale interface couplings of PDEs and ODEs. Her research focuses on the mathematical modeling and analysis of biological and physical systems, particularly in the context of tissue perfusion and eye physiology. She has contributed to understanding the mechanisms underlying glaucoma by modeling the lamina cribrosa within the optic nerve head through multiscale interface coupling techniques, aiming to inform therapeutic approaches for the disease. Dr. Bociu has been involved in multiple research projects funded by the National Science Foundation, including studies on multi-scale interface coupling between deformable porous media and hydraulic circuits, and control and sensitivity analysis for fluid-elasticity interactions and fluid-solid mixtures. Her work bridges applied and computational mathematics, utilizing analysis, control theory of PDEs, micro-local analysis, and shape analysis. She actively disseminates her research through courses, outreach programs, and public exhibits, aiming to foster STEM competency and increase diversity in the field. Her broader impact efforts include engaging with the community through events like Math Doesn’t Bug Me at the NC Museum of Natural Sciences and GAMMA Day at NC State, promoting science literacy and inspiring future generations of STEM students.

Research topics

• Mathematical analysis
• Mathematics
• Geotechnical engineering
• Geology
• Geometry
• Mechanics
• Physics

Selected publications

• Existence and uniqueness of weak solutions to multiscale interface couplings of PDEs and ODEs for tissue perfusion

  Journal of Mathematical Analysis and Applications · 2026-01-14

  article1st authorCorresponding
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• Infinite Horizon Control Problems for Semilinear Parabolic Equations with Pointwise State Constraints

  Applied Mathematics & Optimization · 2026-03-16

  articleOpen access1st authorCorresponding

  Abstract We study an optimal control problem for semilinear parabolic equations with infinite horizon, pointwise state contraints and two different types of control constraints (pointwise in space and time, and pointwise in time and $$L^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> in space). First we prove first-order necessary conditions, then we provide a second-order sufficient condition for local optimality. The second-order condition is formulated using an extended cone that considers the infinite horizon and the control and state constraints. This condition is sufficient for strict local optimality in the $$L^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> -sense. Finally, we address the approximation of the infinite horizon control problem by finite horizon problems. We analyze the convergence of these approximations and provide error estimates.

  PublisherDOI

• Two-point boundary value problems for quasi-monotone dynamical systems

  Discrete and Continuous Dynamical Systems · 2026-01-01

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  This paper studies the existence of minimal solutions to two-point boundary value problems for quasi-monotone dynamical systems. Specifically, the pointwise infimum of all supersolutions is shown to coincide with the minimal solution. This result is then applied to establish a non-uniqueness result for strong solutions to a class of mean field games with a continuum of players.

  PublisherOA PDFDOI

• A theoretical model for the influence of age, race and ethnicity on retinal mitochondria dysfunction

  Journal of Theoretical Biology · 2026-05-15

  articleOpen access

  decreases with A, with a maximum decrease of 37.84% and 32.4% for AA and WE subjects, respectively. Model predictions are consistent with clinical observations indicating higher glaucoma prevalence and severity in older individuals and in specific population groups, and strengthen the view of glaucoma as a multifactorial neurodegenerative disease in which metabolic vulnerability may represent one contributing pathway.

  PublisherDOI

• A Theoretical Model for the Influence of Age, Race and Ethnicity on Retinal Mitochondria Dysfunction

  SSRN Electronic Journal · 2026-01-01

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  PublisherDOI

• Fostering STEM competency in high-school students by bridging engineering and ophthalmology through eye research

  Proceedings of the European Academy of Sciences and Arts · 2025-09-03

  articleOpen accessCorresponding

  Recent data across the globe indicates a decline in stem competency among secondary education students. Despite persistent interest in STEM fields this decrease in preparedness could yield detrimental effects for both future scientists and engineers. To address this current trend, a collaborative partnership between a university and high school commenced. The goal was to create an advanced experiential engineering course focused primarily on ophthalmology principles, research, and hands-on solutions. Twenty-one high school students (grades 9-12) enrolled in the course. Their objective was to investigate research questions involving ocular physiology. These ranged from surveying intraocular pressure measurement methods, examining the nature of vitreous humor properties, and investigating the inherent connection between blood flow and fluid dynamics. Furthermore, students engaged in hands-on experimentation that resulted in a hydraulics-based model which attempted to link the correlation between blood pressure and intraocular pressure involved in glaucoma progression. Post-course interviews revealed three major themes: i) an increased appreciation for the utility of mathematics and its real-world use; ii) the importance of the mentor-mentee relationship and professional networking; and iii) increased access to resources beyond what is traditionally found in a high school classroom. These findings suggest that incorporating research into a high school classroom can foster positive outcomes and spark students’ interest in ophthalmology research and in STEM more broadly. This course can serve as a model in future development of project-based engineering curriculum and help broaden participation in STEM.

  PublisherOA PDFDOI

• Comparing Interface Conditions for a <scp>3D</scp>–<scp>0D</scp> Multiscale Interface Coupling With Applications in Tissue Perfusion

  International Journal for Numerical Methods in Biomedical Engineering · 2025-02-01 · 1 citations

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  Many pathologies are related to hemodynamic changes occurring at the microvascular level, where small vessels pierce the tissue, perfusing it with blood. Since there is a large number of vessels of small caliber, it is impractical to model the fluid flow through each one of them separately, as it is done in the case of large arteries using, for example, the Navier-Stokes equations. As an alternative, tissue perfusion is modeled here via three-dimensional (3D) partial differential equations (PDEs) for fluid flow through deformable porous media, where blood vessels are modeled as pores within a deformable solid representing the tissue. Since it is known that the local perfusion is related to the systemic features of surrounding blood circulation, we couple the PDE system with a zero-dimensional (0D) lumped circuit model, obtained by the analogy between fluid flows in hydraulic networks and current flowing in electrical circuits. An important feature in this multiscale 3D-0D coupling is the specification of interface conditions between the 3D and the 0D parts of the system. In this article, we focus on two types of interface conditions driven by physical considerations, and compare the behavior of the solutions for the two different scenarios.

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• Analysis of a Multiscale Interface Problem Based on the Coupling of Partial and Ordinary Differential Equations to Model Tissue Perfusion

  Multiscale Modeling and Simulation · 2025-01-03 · 2 citations

  articleOpen access1st authorCorresponding

  In biomechanics, local phenomena, such as tissue perfusion, are strictly related to the global features of the surrounding blood circulation. In this paper, we propose a heterogeneous model where a local, accurate, 3D description of tissue perfusion by means of fluid flows through deformable porous media equations is coupled with a systemic, 0D, lumped model of the remainder of the circulation, where the fluid flow through a vascular network is described via its analog with a current flowing through an electric circuit. This represents a multiscale strategy, which couples an initial boundary value problem to be used in a specific tissue region with an initial value problem in the surrounding circulatory system. This PDE/ODE coupling leads to interface conditions enforcing the continuity of mass and the balance of stresses across models at different scales, and careful consideration is taken to address this interface mismatch. The resulting system involves PDEs of mixed type with interface conditions depending on nonlinear ODEs. A new result on local existence of solutions for this multiscale interface coupling is provided in this article.

  PublisherOA PDFDOI

• Input Regularization for Integer Optimal Control in BV with Applications to Control of Poroelastic and Poroviscoelastic Systems

  Journal of Nonsmooth Analysis and Optimization · 2024-04-29 · 2 citations

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  We revisit a class of integer optimal control problems for which a trust-region method has been proposed and analyzed in arXiv:2106.13453v3 [math.OC]. While the algorithm proposed in arXiv:2106.13453v3 [math.OC] successfully solves the class of optimization problems under consideration, its convergence analysis requires restrictive regularity assumptions. There are many examples of integer optimal control problems involving partial differential equations where these regularity assumptions are not satisfied. In this article we provide a way to bypass the restrictive regularity assumptions by introducing an additional partial regularization of the control inputs by means of mollification and proving a $\Gamma$-convergence-type result when the support parameter of the mollification is driven to zero. We highlight the applicability of this theory in the case of fluid flows through deformable porous media equations that arise in biomechanics. We show that the regularity assumptions are violated in the case of poro-visco-elastic systems, and thus one needs to use the regularization of the control input introduced in this article. Associated numerical results show that while the homotopy can help to find better objective values and points of lower instationarity, the practical performance of the algorithm without the input regularization may be on par with the homotopy.

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• Piecewise regular solutions to scalar balance laws with singular nonlocal sources

  Journal of Differential Equations · 2024-07-15

  articleOpen access1st author
  PublisherOA PDFDOI

Recent grants

• International Research Fellowship Program: Hadamard Wellposedness and Asymptotic Stability of Finite Energy Solutions for a Structural Acoustic Interaction Modeled by Nonlinear

  NSF · $198k · 2009–2014

• CAREER: Control and Sensitivity Analysis for Fluid-Elasticity Interactions and Fluid-Solid Mixtures

  NSF · $421k · 2016–2024

• Optimal Control in Coupled Systems with Moving Interfaces

  NSF · $180k · 2013–2017

Frequent coauthors

• Justin T. Webster

  14 shared

• Riccardo Sacco

  13 shared

• Jean-Paul Zolésio

  12 shared

• Maurizio Verri

  University of Missouri

  11 shared

• Giovanna Guidoboni

  11 shared

• Daniel Toundykov

  University of Nebraska–Lincoln

  10 shared

• Boris Muha

  University of Zagreb

  9 shared

• Irena Lasiecka

  8 shared

Labs

• NC State Department of MathematicsPI

Education

• Ph.D., Mathematics

  University of Maryland, College Park

  2006

• M.S., Mathematics

  University of Maryland, College Park

  2002

• B.S., Mathematics

  University of Bucharest

  1999

Awards & honors

• NSF CAREER Award (2016)
• 40th Southeastern-Atlantic Regional Conference on Differenti…