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 CAREER Award DMS-1555062 and NSF DMS – 2108711

Previous Funding: 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, 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.
  2. 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)
  3. 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.
  4. L. Bociu and S. Strikwerda**, Poro-Visco-Elasticity in Biomechanics – Optimal Control, Springer AWM Volume on “Research in the Mathematics of Materials Science”, 2022.
  5. L. Bociu and S. Strikwerda**, Optimal Control in Poroelasticity , Applicable Analysis, 2021, https://doi.org/10.1080/00036811.2021.2008372. Link: https://www.tandfonline.com/eprint/IFEUMKKBQDNTY9BNE6Z2/full?target=10.1080/00036811.2021.2008372
  6. 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.
  7. L. Bociu, J. Webster, Nonlinear Quasi-static Poroelasticity , Journal of Differential Equations, Volume 296, 25, September 2021, 242-278.
  8. 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 .
  9. 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
  10. 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
  11. 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
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
  24. 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
  25. Processing (2013), 445 – 460.
  26. 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.
  27. 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-
  28. 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.
  29. 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.
  30. L. Bociu and D. Toundykov, Attractors for non-dissipative irrotational von Karman plates with boundary damping , Journal of Differential Equations 253 (2012), 3568-3609.
  31. 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.
  32. 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.
  33. 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.
  34. 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.
  35. 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.
  36. 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.
  37. 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.
  38. 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.
  39. 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.
  40. 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.
  41. 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. (with J.A. Desideri and A. Habbal) Springer Series: IFIP Advances in Information and Communication Technology (IFIP AICT Series)- System Modeling and Optimization (CSMO 2017).
  2. (with 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.
  3. (with P. Radu) Evolution Equations and Control Theory, Special Volume on Local and Nonlocal Models in Wave Propagation and Diffusion, 2014.