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]:
- 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.
- 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)
- 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.
- L. Bociu and S. Strikwerda**, Poro-Visco-Elasticity in Biomechanics – Optimal Control, Springer AWM Volume on “Research in the Mathematics of Materials Science”, 2022.
- 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
- 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.
- L. Bociu, J. Webster, Nonlinear Quasi-static Poroelasticity , Journal of Differential Equations, Volume 296, 25, September 2021, 242-278.
- 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 .
- 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
- 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
- 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
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- L. Bociu and D. Toundykov, Attractors for non-dissipative irrotational von Karman plates with boundary damping , Journal of Differential Equations 253 (2012), 3568-3609.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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
- (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).
- (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.
- (with P. Radu) Evolution Equations and Control Theory, Special Volume on Local and Nonlocal Models in Wave Propagation and Diffusion, 2014.