Research and Publications

Analysis, Optimization, and Control in Partial Differential Equations (PDEs):

  • free and moving boundary problems, with focus on fluid-elasticity interactions – well-posedness, sensitivity analysis, optimization, and control.
  • fluid-solid mixture problems, in particular poroelasticity and poro-visco-elasticity  – well-posedness analysis, parameter estimation and control.
  • flow-poroelasticity interactions – well-posedness analysis and control.
  • multiscale interface couplings between poroelastic media and lumped hydraulic circuits – well-posedness, numerical methods for solutions.
  • hyperbolic problems with Neumann boundary conditions – shape differentiability analysis
  • evolutionary PDEs (nonlinear waves, shells, thermoelastic systems, etc.) under the influence of super-critical energy-building sources and nonlinear, potentially restricted damping terms – well-posedness, regularity, and long-time behavior.

Current Funding: NSF DMS 2510261

Previous Funding: NSF CAREER Award DMS-1555062, NSF DMS – 2108711,NSF -OISE 0802187; NSF DMS – 1312801

Publications available on arXiv

Publications [*: postdoc, **: graduate student, ***: undergraduate; at the time the paper was submitted]:

  1. L. Bociu and E. Casas, Infinite Horizon Control Problems for Semilinear Parabolic Equations with Pointwise State Constraints, Applied Mathematics and Optimization (AMOP) (2026) 93:55, DOI:10.1007/s00245-026-10411-5
  2. A. Alalabi* and L. Bociu, Optimal Control in Poroelastic Systems via E-Radiality Theory, The 2026 American Control Conference (ACC) Proceedings.
  3. A. Alalabi*, L. Bociu, B. Jacob, and K. Morris, Wellposedness of Irregular Infinite–Dimensional Differential-Algebraic Equations, The 2026 European Control Conference.
  4. L. Bociu and G. Guidoboni, Multiscale Interface Coupling of Partial and Ordinary Differential Equations for Modeling Tissue Perfusion, Springer Volume “Proceedings of 2023 AWM Research Symposium”, Springer “Association for Women in Mathematics Series”, in press 2026.
  5. L. Bociu, K.T. Nguyen, and M. Roy*, Two-Point Boundary Value Problems for Quasi-Monotone Dynamical Systems, Discrete and Continuous Dynamical Systems, 2026, doi:10.3934/dcds.2026088
  6. R. Sacco, K. Wood, G. Guidoboni, R. Rai**, K. Tilbury, L. Bociu, G. Antman, A. Verticchio Vercellin, B. Siesky, T. Ciulla, and A. Harris, A Theoretical Model for the Influence of Age, Race and Ethnicity on Retinal Mitochondria Dysfunction, Journal of Theoretical Biology, 2026, http://dx.doi.org/10.2139/ssrn.6182535
  7. L. Bociu, M. Broussard**, and S. Strikwerda*, Existence and Uniqueness of Weak Solutions to Multiscale Interface Couplings of PDEs and ODEs for Tissue Perfusion, Journal of Mathematical Analysis and Applications (JMAA), Vol. 558, Issue 1, June 2026, 130409, DOI: 10.1016/j.jmaa.2026.130409.
  8. K. Real, G. Guidoboni, R. Rai**, H.C. White, S. Abbadessa, M. Murphy, G. Aulisa***, L. Hart, E. Marquis, L. Bociu, and A. Harris, Fostering STEM Competency in High-School Students by Bridging Engineering and Ophthalmology through Eye Research, Proceedings of the European Academy of Sciences & Arts (PEASA) 2025, Vol. 4:59, DOI:10.4081/peasa.59
  9. L. Bociu, M. Broussard**, G. Guidoboni, D. Prada, and S. Strikwerda*, Comparing Interface Conditions for a 3D-0D Multiscale Interface Coupling with Applications in Tissue Perfusion, International Journal for Numerical Methods in Biomedical Engineering, Volume 41, Issue 2 DOI 10.1002/cnm.70017. Published: February 2025.
  10. L. Bociu, M. Broussard**, G. Guidoboni, and S. Strikwerda, Analysis of a Multiscale Interface Problem Based on the Coupling of Partial and Ordinary Differential Equations to Model Tissue Perfusion, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Vol. 23, no. 1, pp. 1–24, 2025.
  11. L. Bociu, Evangelia Ftaka**, Khai Nguyen, and Jacopo Schino*, Piecewise smooth solutions to scalar balance laws with singular nonlocal sources, Journal of Differential Equations, Volume 409, 15 Nov. 2024, p. 181-222.
  12. L. Bociu, P. Manns, M. Severitt**, S. Strikwerda**,Input Regularization for Integer Optimal Control in BV with Applications to Control of Poroelastic and Poroviscoelastic Systems, Journal of Nonsmooth Analysis and Optimization, 5 (2024), 10529, doi:10.46298/jnsao-2024-10529.
  13. C. Hendrick, L. Bociu, A. Harris, R. Rai, M. Zaid, and G. Guidoboni, Interactive webinar for high school students connecting physics and ophthalmology, Investigative Ophthalmology & Visual Science (IOVS) June 2024, Vol.65(7): 4216.
  14. M. Murphy, G. Guidoboni, G. Aulisa, L. Hart, E. Marquis, L. Bociu, and A. Harris, Inspiring interest in eye research by bridging engineering and ophthalmology in high school, Investigative Ophthalmology & Visual Science (IOVS)June 2024, Vol.65(7): 4217.
  15. Prada, R. Sacco, B. Cockburn, L. Bociu, J. Webster, B. Siesky, A. Harris, and G. Guidoboni, Influence of Tissue Viscoelasticity on the Optic Nerve Head Perfusion: A Mathematical Model, Investigative Ophthalmology & Visual Science (IOVS)June 2024, Vol.57(12): 3358.
  16. L. Bociu, B. Muha, and J. Webster, Mathematical Effects of Linear Visco-elasticity in Quasi-static Biot Models, Journal of Mathematical Analysis and Applications, Volume 527, Issue 2, 15 November 2023, 127462.
  17. L. Bociu, G. Guidoboni, R. Sacco, and D. Prada, Numerical simulation and analysis of multiscale interface coupling between a poroelastic medium and a lumped hydraulic circuit: comparison between functional iteration and operator splitting methods, Journal of Computational  Physics,  Vol. 466,  1 October 2022, 111379;  Available at https://authors.elsevier.com/c/1fN8C508HsZd1 (until August 26, 2022)
  18. L. Bociu, B. Muha, and J. Webster, Weak Solutions in Nonlinear Poroelasticity with Incompressible Constituents, Nonlinear Analysis: Real World Applications, 67, 2022. Available at https://arxiv.org/abs/2108.10977.
  19. L. Bociu and S. Strikwerda**, Poro-Visco-Elasticity in Biomechanics – Optimal Control, Springer AWM Volume on “Research in the Mathematics of Materials Science”, 2022.
  20. L. Bociu and S. Strikwerda**, Optimal Control in Poroelasticity , Applicable Analysis, 2021, https://doi.org/10.1080/00036811.2021.2008372.
  21. L. Bociu, S. Canic, B. Muha, J. Webster, Multilayered Poroelasticity Interacting with Stokes Flow, SIAM J. Math. Anal., 53(6), 2021,p. 6243–6279, https://doi.org/10.1137/20M1382520.
  22. L. Bociu, J. Webster, Nonlinear Quasi-static Poroelasticity , Journal of Differential Equations, Volume 296, 25, September 2021, 242-278.
  23. L. Bociu, L. Castle*, I. Lasiecka, and A. Tuffaha, Minimizing Drag in A Moving Boundary Fluid-Elasticity Interaction , Nonlinear Analysis 197 (2020), 41pp., https://doi.org/10.1016/j.na.2020.111837 .
  24. L. Bociu, G. Guidoboni, R. Sacco, and M. Verri, On the Role of Compressibility in Poroviscoelastic Models, Mathematical Biosciences and Engineering , July 2019, 16(5): 6167-6208. DOI: 10.3934/mbe.2019308
  25. L. Bociu and M. Noorman**, Poro-Visco-Elastic Models in Biomechanics: Sensitivity Analysis , Communications in Applied Analysis, Vol.23, No 1 (2019), 61-77. DOI: 10.12732/caa.v23i1.5
  26. H.T. Banks, K. Bekele-Maxwell*, L. Bociu, M. Noorman**, and G. Guidoboni, Local sensitivity via the complexstep derivative approximation for 1-D poro-elastic and poro-visco-elastic models , Mathematical Control and Related Fields, Volume 9, Number 4, December 2019, 9(4): 623-642. DOI: 10.3934/mcrf.2019044
  27. M. Verri, G. Guidoboni, L. Bociu and R. Sacco, The Role of Structural Viscosity in Deformable Porous Media with Applications in Biomechanics , Mathematical Biosciences and Engineering, Vol. 15, No. 4, August 2018, 933-959.
  28. L. Bociu, S. Derochers**, and D. Toundykov, Feedback Stabilization of a Linear Hydro-Elastic System , Discrete and Continuous Dynamical Systems – B, Vol. 23, No. 3, May 2018, 1107-1132.
  29. H.T. Banks, K. Bekele-Maxwell*, L. Bociu, Marcella Noorman**, and G. Guidoboni, Sensitivity Analysis in Poro-Elastic and Poro-Visco-Elastic Models with Respect to Boundary Data , Quart. Appl. Math., Vol. LXXV, No. 4, December 2017, 697-735.
  30. H.T. Banks, K. Bekele-Maxwell*, L. Bociu, and Chuyue Wang***, Sensitivity via the complex-step method for delay differential equations with non-smooth initial data, Quart. Appl. Math. 75  (2017), 231-248.
  31. L. Bociu, G. Guidoboni, R. Sacco, and J. Webster*, Analysis of nonlinear poro-elastic and poro-visco-elastic models , Archive for Rational Mechanics and Analysis, 222 (2016), 1445-1519. DOI: 10.1007/s00205-016-1024-9.
  32. L. Bociu, S. Derochers**, and D. Toundykov, Linearized Hydro-Elasticity: A Numerical Study , Evolution Equations and Control Theory, Vol. 5, Number 4 (December 2016), 533-559.
  33. L. Bociu and K. Martin**, Free Boundary Fluid-Elasticity Interactions: Adjoint Sensitivity Analysis , New Trends in Differential Equations, Control Theory and Optimization, 2016, 21-39.
  34. L. Bociu and J.-P. Zolesio, Hyperbolic equations with mixed boundary conditions: shape differentiability analysis,  Applied Mathematics and Optimization, 2016, published online: DOI 10.1007/s00245-016-9354-4.
  35. L. Bociu, D. Toundykov, and J.-P. Zolesio, Well-posedness analysis for the total linearization of a fluid-elasticity interaction,  SIAM Journal of Mathematical Analysis 47-3 (2015), 1958 – 2000.
  36. L. Bociu, L. Castle**, K. Martin**, and D. Toundykov, Optimal Control in a Free Boundary Fluid-Elasticity Interaction , Dynamical Systems, Differential Equations and Applications AIMS Proceedings, 2015, 122 – 131.
  37. H.T. Banks, K. Bekele-Maxwell*, L. Bociu, M. Noorman**, and K. Tillman**, The complex-step method for sensitivity analysis of non-smooth problems arising in biology , Eurasian Journal of Mathematical and Computer Applications ISSN 2306-6172, Volume 3, Issue 3 (2015), 16 – 68.
  38. L. Bociu and J.-P. Zolesio, A Pseudo-Extractor Approach to Hidden Boundary Regularity for the Wave Equation with Mixed Boundary Conditions,  Journal of Differential Equations 259 (2015), no. 11, 5688 – 5708.
  39. J.-P. Zolesio and L. Bociu, Strong shape derivative for the wave equation with Neumann boundary condition , D. Homberg and F. Troltzsch (Eds.): CSMO 2011, IFIP AICT 391, International Federation for Information Processing (2013), 445 – 460.
  40. L. Bociu and D. Toundykov, Wave equations with nonlinear sources and damping: weak vs. regular solutions, Palestine Journal of Mathematics, Vol.2(2) (2013), 175-186.
  41. L. Bociu, P. Radu, and D. Toundykov, Regular solutions of wave equations with super-critical sources and exponential-to-logarithmic damping,  Evolution Equations and Control Theory, Vol. 2, no. 2, June 2013, 255-279. With Errata: Regular solutions of wave equations with super-critical sources and exponential-to-logarithmic damping , EECT, Vol.3, no. 2, June 2014, 349-354.
  42. L. Bociu and J.-P. Zolesio, Sensitivity analysis for a free boundary fluid-elasticity interaction , Evolution Equations and Control Theory Volume 2, Number 1, 2013, 55-79.
  43. L. Bociu and D. Toundykov, Attractors for non-dissipative irrotational von Karman plates with boundary damping , Journal of Differential Equations 253 (2012), 3568-3609.
  44. L. Bociu*, M. Rammaha, and D. Toundykov, Wave equations with super-critical interior and boundary nonlinearities, Mathematics and Computers in Simulation Vol. 82, Issue 6 (Feb. 2012), pp. 1017-1029.
  45. L. Bociu* and J.-P. Zolesio, Existence for the linearization of a steady state fluid – nonlinear elasticity interaction , Discrete and Continuous Dynamical Systems, Supplement Sept. 2011, 184-197.
  46. L. Bociu*, M. Rammaha, and D. Toundykov, On a wave equation with supercritical interior and boundary sources and damping terms , L. Bociu, M. Rammaha, and D. Toundykov, Mathematische Nachrichten Vol. 284, Issue 16 (Aug. 2011), 2032-2064.
  47. L. Bociu* and J.-P. Zolesio, Linearization of a coupled system of nonlinear elasticity and viscous fluid , “Modern Aspects of the Theory of Partial Differential Equations – Operator Theory: Advances and Applications”, Vol. 216, Springer, Basel, May 2011, 93-120.
  48. L. Bociu* and I. Lasiecka, Hadamard Wellposedness for Nonlinear Wave Equations with Supercritical Sources and Damping , J. Differential Equations Vol. 249, Issue 3 (August 2010), 654-683.
  49. L. Bociu*, Local and Global Wellposedness of Weak Solutions for the Wave Equation with Nonlinear Boundary and Interior Sources of Supercritical Exponents and Damping , Nonlinear Analysis Series A: Theory, Methods and Applications, Vol. 71, Issue 12 (2009), e560–e575.
  50. L. Bociu* and P. Radu, Existence and Uniqueness of Weak Solutions to the Cauchy Problem of a Semilinear Wave Equation with Supercritical Interior Source and Damping , Dynamical Systems and Differential Equations – S (2009), 60-71.
  51. L. Bociu**, Existence, uniqueness and blow-up of solutions to wave equations with supercritical boundary/interior sources and damping. Thesis (Ph.D.)–University of Virginia. 2008, 98 pp. ISBN: 978-0549-60005-3.
  52. L. Bociu** and I. Lasiecka, Blow-up of Weak Solutions for the Semilinear Wave Equations with Nonlinear Boundary and Interior Sources and Damping , Applicationes Mathematicae, 35,3 (2008), 281-304.
  53. L. Bociu** and I. Lasiecka, Uniqueness of Weak Solutions for the Semilinear Wave Equations with Supercritical Boundary/Interior Sources and Damping , Discrete and Continuous Dynamical Systems 22(4) (2008), 835-860.
  54. L. Bociu** and I. Lasiecka, Wellposedness and Blow-up of Solutions to Wave Equations with Supercritical Boundary Sources and Boundary Damping , Proceedings of the Conference on Differential and Difference Equations and Applications (2006), Hindawi Publishing Corporation, 635-643.

 

Co-Edited Special Volumes

  1. L. Bociu and G. Fragnelli, Communications in Analysis and Mechanics – Special Issue: New trends in Control Theory, Stability, PDEs and Applications https://www.aimspress.com/cam/article/6511/special-articles

  2. L. Bociu, C. Pignotti, and C. Prieur, 2023 Proceedings of the Conference on Control and Its Applications (CT).
  3. L. Bociu, J.A. Desideri and A. Habbal, Springer Series: IFIP Advances in Information and Communication Technology (IFIP AICT Series)- System Modeling and Optimization (CSMO 2017).
  4. L. Bociu, B. Kaltenbacher and P. Radu, Evolution Equations and Control Theory, Special Volume on Nonlinear PDEs and Control Theory with Applications, Vol. 2, No 2, 2013.
  5. L. Bociu and P. Radu, Evolution Equations and Control Theory, Special Volume on Local and Nonlocal Models in Wave Propagation and Diffusion, 2014.