I study coupled systems of partial differential equations where interaction is the mechanism that creates instability, transmits dissipation, or elicits resonance. My PhD work, advised by Irena Lasiecka, provided training in PDE control and stability. I fall into the school of Lasiecka and Roberto Triggiani, where semigroup, spectral, and nonlinear dynamical-systems methods are at the core. Through work with Lasiecka, Igor Chueshov, Earl Dowell, and A.V. Balakishnan, I participated in the analytical foundations of mathematical aeroelasticity, including well-posedness and regularity theory, flutter suppression, post-flutter qualitative studies, and stabilization for nonlinear flow-structure systems. Postdoctoral work with Ralph Showalter and Małgorzata Peszyńska introduced me to implicit and degenerate evolution equations and to the modern theory of poroelasticity; subsequent collaborations with Lorena Bociu and others extended that perspective to nonlinear, viscoelastic, multilayer, and fluid-coupled systems. Across these areas, a recurring goal is to develop weak-solution and semigroup frameworks which reveal what PDE coupling preserves, transfers, or destroys between interactive components. My more recent work focuses on partially dissipative systems, where nonuniform decay and periodic forcing expose hidden losses of regularity. I have particularly adopted the point of view of Paolo Galdi, which links the decay properties of homogeneous solution semigroups with periodic well-posedness properties. In particular, I am presently developing criteria to connect resolvent growth, periodic solvability, and secular resonance, and then applying these to weakly damped systems. We have recently discovered some surprising and exciting connections with control theory, and uncovered the simultaneous prevalence and pathological nature of resonance. Selected Contributions Complete Publications
JTW Research, Collaboration, and Mentorship Tree: LINK (updated July 2026)
My research program has been externally supported by several National Science Foundation projects. I have two current awards. First, Self-excitation, Limit Cycle Oscillations, and Control of Large Deflection Plate Models in Engineering Applications (DMS-2307538, 2023--2027), concerns nonlinear structural models that generate and sustain oscillations through nonconservative feedbacks. Secondly, Regularity, Stability, and Control of Poroelastic Filtrations (DMS-2606567, 2026--2029) is collaborative with George Avalos at UNL, DMS-2606568 and aims to develop foundational regularity and stability theories for poro-elastic filtrations. The collaborative project Aeroelastic Limit Cycle Oscillations for Energy Harvesting Applications linked the UMBC award DMS-1907620 with companion awards at Duke and Carnegie Mellon. Earlier awards DMS-1412238 and DMS-1504697, Analysis and Control of Mathematical Models of Fluttering Plates, supported the foundational flow-plate and flutter-control work which formed the basis of my early research and is described below.
Mathematical Aeroelasticity and Self-Destabilizing Systems
Nonlinear flow-plate well-posedness and long-time dynamics. My early work provided semigroup and dynamical-systems frameworks for nonlinear elastic plates interacting with subsonic and supersonic potential flows. These results treated the coupled flow and structure as a single evolution, established weak and strong solutions, and developed delayed-dynamics reductions revealing finite-dimensional long-time asymptotics, even when no mechanical damping is invoked in the structural model. Representative papers include Weak and Strong Solutions of a Nonlinear Subsonic Flow-Structure Interaction: Semigroup Approach, Nonlinear Analysis (2011); Evolution Semigroups in Supersonic Flow-Plate Interactions, Journal of Differential Equations (2013); Attractors for Delayed, Non-rotational von Karman Plates with Applications to Flow-Structure Interactions without Any Damping, Communications in PDE (2014); and Attractors and Determining Modes for a Panel Flutter Model: Finite Dimensionality out of Thin Air, Pure and Applied Functional Analysis (2020).
Self-destabilization, flutter suppression, and damping transmission. Aeroelastic systems can be self-destabilizing: the flow coupling acts as a nonconservative feedback and can generate flutter. My work with Irena Lasiecka and Abhishek Balakrishna developed component-wise control and stabilization mechanisms, showing how structural feedback or weak plate damping can suppress instability and, in a fully three-dimensional potential-flow model, stabilize the entire coupled system. This line connects aeroelastic control to the broader problem of indirect damping in coupled hyperbolic dynamics. Microlocal analysis methods are critical for these analyses, focusing on hidden regularity present for hyperbolic traces in coupled flow-plate models. Anchor papers are Eliminating Flutter in Clamped von Karman Plates Immersed in Subsonic Flows, Communications on Pure and Applied Analysis (2014); Feedback Stabilization of a Fluttering Panel in an Inviscid Subsonic Potential Flow, SIAM Journal on Mathematical Analysis (2016); Strong Stabilization of a 3D Potential Flow via a Weakly Damped von Karman Plate, Mathematical Models and Methods in Applied Sciences (2023); and Flutter Stabilization for an Unstable, Hyperbolic Flow-Plate Interaction, in Fluids under Control (2024).
Post-flutter dynamics and large-deflection structures. Beyond the onset of flutter, I have developed and analyzed nonlinear models for panels, cantilevers, inextensible beams and plates, and bridge sections, with emphasis on post-flutter regimes, attractors, and the qualitative fidelity of structural reductions. This program combines rigorous PDE analysis with computation and engineering modeling, including vibration-based energy-harvesting applications. Representative papers include A Cantilevered Extensible Beam in Axial Flow: Semigroup Solutions and Post-flutter Regimes, SIAM Journal on Mathematical Analysis (2018); Large Deflections of Inextensible Beams: Modeling, Theory, and Simulation, Mathematical Modelling of Natural Phenomena (2020); Theory of Solutions for an Inextensible Cantilever, Applied Mathematics and Optimization (2021); and Large Deflections of a Flow-Driven Cantilever with Kutta-Joukowski Flow Conditions, Discrete and Continuous Dynamical Systems-S (2026).
Compressible and open-flow fluid-structure interaction. A separate line of work extended semigroup and weak-solution methods to viscous compressible flows interacting with elastic boundaries, where non-dissipative coupling, pressure, and open-flow boundary conditions create difficulties absent from classical incompressible models. This includes Semigroup Well-posedness of a Linearized, Compressible Fluid with an Elastic Boundary, Discrete and Continuous Dynamical Systems-B (2018); A Linearized Viscous, Compressible Flow-Plate Interaction with Non-dissipative Coupling, Journal of Mathematical Analysis and Applications (2019); and Steady Weak Solutions for a Plate Coupled to Compressible Viscous Flow with Inflow-Outflow Boundary Conditions (2026).
Partial Dissipation, Stability, Periodicity, and Resonance
Stability-to-periodicity principles for coupled evolution equations. This program asks how decay of an evolution semigroup governs solvability under time-periodic forcing, especially when dissipation acts on only a certain component of a coupled system. Work with Stanislav Mosný, Boris Muha, and Sebastian Schwarzacher established periodic solutions for hyperbolic-parabolic systems. More recent work with Paolo Galdi and Muha extends the stability-periodicity program from uniformly stable dynamics to polynomially stable and partially dissipative regimes, quantifying the temporal regularity loss required for periodic solvability. Related work clarifies the weak-solution framework and the distinction between periodic solvability and secular resonance. Ongoing work will provide a complete taxonomy of infinite dimensional resonance behaviors, quantified in terms of so called ``derivative loss." Representative papers are An Observation about Weak Solutions of Linear Differential Equations in Hilbert Spaces, Applied Mathematics and Optimization (2024); Time-Periodic Solutions for Hyperbolic-Parabolic Systems, accepted in the Journal of the European Mathematical Society (2026); From Polynomial Stability to Periodic Well-Posedness in Partially Dissipative Systems (2026); and Resonance and Periodic Solutions for Harmonic Oscillators with General Forcing, accepted in the education section of SIAM Review (2025).
Modern Analytical Poroelasticity
Nonlinear and degenerate Biot systems. My poroelasticity work continues the implicit-evolution tradition associated with Ralph Showalter and extends it to nonlinear constitutive laws, incompressible constituents, degeneracy, and viscoelastic regularization. With collaborators, I have helped establish weak-solution theories for nonlinear Biot systems and identify precisely how structural regularization changes existence, uniqueness, and regularity properties of the dynamics. Anchor papers include Analysis of Nonlinear Poro-elastic and Poro-visco-elastic Models, Archive for Rational Mechanics and Analysis (2016); Nonlinear Quasi-static Poroelasticity, Journal of Differential Equations (2021); Weak Solutions in Nonlinear Poroelasticity with Incompressible Constituents, Nonlinear Analysis: Real World Applications (2022); and The Mathematical Effects of Visco-elasticity in Quasi-static Biot Models, Journal of Mathematical Analysis and Applications (2023).
Poroelastic structures and fluid-poroelastic interaction. I have extended Biot theory to reduced-dimensional poroelastic plates, multilayer structures, and filtration systems coupling poroelastic solids to free Stokes flow. The resulting work includes weak solutions for implicit poroelastic plates, nonlinear multilayer filtrations, semigroup constructions of weak and strong solutions, and uniqueness for Biot-Stokes interaction. Representative papers are Weak Solutions for a Poro-elastic Plate System, Applicable Analysis (2021); Multilayered Poroelasticity Interacting with Stokes Flow, SIAM Journal on Mathematical Analysis (2021); Weak and Strong Solutions for a Fluid-Poroelastic-Structure Interaction via a Semigroup Approach, Mathematical Methods in the Applied Sciences (2024); and Uniqueness of Weak Solutions for Biot-Stokes Interactions, Pure and Applied Analysis (2025).
(updated - July 2026)
Books/Book Chapters
(with I. Lasiecka),
Flutter Stabilization For An Unstable, Hyperbolic Flow-Plate Interaction
In: Fluids under Control, Brikhauser; 2024.
(with B. Kaltenbacher, I. Kukavica, I. Lasiecka, R. Triggiani, and A. Tuffaha),
Mathematical Theory of Flow/Fluid-Structure Interactions
In: Oberwolfach Seminars, Springer; 2018.
Special Volumes Edited
(with I. Lasiecka and R. Triggiani), PDE Control: From Classical to Emerging Themes and Methods,
guest editorial introducing a special collection in Research in the Mathematical Sciences, Volume 12, Article 52, 2025.
(with M. Disconzi and D. Toundykov), Evolution Equations and Control Theory
Special volume on fluid-structure interactions, Volume 5, 4, 2016,
arising from the 2015 SIAM Conference on Analysis of PDEs.
Preprints and Submitted Articles
(with P. Lavagnino and A. Lee) Weak Solutions and Inertial Limits for Quasi-static Filtrations,
submitted May 2026.
(with P. Galdi and B. Muha) From polynomial stability to periodic well-posedness in partially
dissipative systems, submitted May 2026.
(with B. Muha, Š. Nečasová, M. Pokorny, Srdjan Trifunović) Steady Weak Solutions for A Plate Coupled
to Compressible Viscous Flow with Inflow-Outflow Boundary Conditions, under revision July 2026.
Accepted and Forthcoming Articles
(with S. Mosný, B. Muha, and S. Schwarzacher) Time-Periodic Solutions for Hyperbolic-Parabolic Systems,
J. European Mathematical Society accepted May 2026.
(with G. Avalos and G. Richard) Semigroup Generation for Multilayered Filtrations,
Contemporary Mathematics accepted March 2026.
(with I. Benson) Resonance and Periodic Solutions for Harmonic Oscillators with General Forcing,
SIAM Review (Education Section) accepted Dec. 2025.
Published Peer-reviewed Articles
(with M. Deliyianni and I. Lasiecka) Large Deflections of A Flow-Driven Cantilever
with Kutta-Joukowski Flow Conditions, Discrete and Continuous Dynamical Systems-S,
Volume 26, 2026, pp. 153--187.
(with G. Avalos) Uniqueness of Weak Solutions for Biot-Stokes Interactions, Pure and Applied Analysis,
Vol. 7 (4), 2025, pp. 1111--1139.
(K. Hoffman, T. Williams, J.T. Webster, J. Harrison, K. Nanes) Assessing the Impact of An Interventional
Proof-Writing Course, International Journal of Mathematical Education in Science and Technology ,
Vol. 57 (3), 2026, pp. 466--490.
(with A. Falocchi) Analysis of a nonlinear fish-bone model for suspension bridges with rigid hangers in the
presence of flow effects, Discrete and Continuous Dynamical Systems, Volume 45(7), 2025, pp.2241--2280.
(with V. Pata) An Observation About Weak Solutions of Linear Differential Equations in Hilbert Spaces,
Applied Mathematics and Optimization, Volume 90, 2024.
(with G. Avalos and E. Gurvich) Weak and Strong Solutions for a Fluid-Poroelastic-Structure Interaction
via a Semigroup Approach, Mathematical Methods in the Applied Sciences , Vol. 48 (4), 2024, pp.4057--4089.
(with L. Bociu and B. Muha) The Mathematical Effects of Visco-elasticity in Quasi-static Biot Models
J. Mathematical Analysis and Applications Volume 527(2), 2023.
(with A. Balakrishna and I. Lasiecka) Strong Stabilization of a 3D Potential Flow via a
Weakly Damped von Karman Plate, Mathematical Models and Methods in Applied Sciences,
Volume 33 (3), 2023.
(with L. Bociu and B. Muha) Weak Solutions in Nonlinear Poroelasticity with Incompressible Constituents
Nonlinear Analysis Real World Applications Volume 67, Oct. 2022.
(with M. Deliyianni, E. Dowell, and K. McHugh) Dynamic Equations of Motion
for Inextensible Beams and Plates, Archive of Applied Mechanics, 92(6), 2022, pp.1 929--1952.
(with D. Bonheure, F. Gazzola, and I. Lasiecka) Long-time dynamics of a hinged-free plate driven by a
non-conservative force., Annales de l’Institut Henri Poincare, Analy. NonLin, 39 (2), 2022, pp. 457--500.
(with M. Deliyianni) Theory of solutions for an inextensible cantilever.
Applied Mathematics and Optimization, published online 2021.
(with E. Gurvich) Weak Solutions for a Poro-elastic Plate System,
Applicable Analysis 101 (5), 2021, pp. 1617--1636.
(with L. Bociu) Nonlinear quasi-static poroelasticity. J. Differential Equations,
296 (25), 2021, pp. 242-–278.
(with L. Bociu, S. Canic, and B. Muha) Multilayered poroelasticity interacting with Stokes flow.
SIAM J. Mathematical Analysis, 53 (6), 2021, 6243--6279.
(with M. Deliyianni, V. Gudibanda, and J. Howell) Large deflections of inextensible beams:
modeling, theory, and simulation, Math. Model. Nat. Phenom., 15, (44), 2020.
(with A. Balakrishna) Large Deflections of A Structurally Damped Panel in A Subsonic Flow,
Nonlinear Dynamics, 103, 2021, 3165--3186.
Attractors and determining modes for a panel flutter model: Finite dimensionality out of thin air,
Pure and Appl. Funct. Analy. , 5 (1), 2020, pp. 85--119.
(with K. Huneycutt, J. Howell, and S. Wilder) (In)stability of thin beams in a potential flow, Math. in Engin.,
1 (3), 2019, pp. 614-–647.
(with G. Avalos and P. G. Geredeli) A linearized viscous, compressible flow-plate interaction with
non-dissipative coupling, J. Mathem. Analy. Appl., Volume 477, 1, 2019, pp. 334--356.
(with J. Howell and D. Toundykov) A Cantilevered Extensible Beam in Axial Flow: Semigroup Solutions and
Post-flutter Regimes, SIAM J. Mathem. Analys., Volume 50, 2, 2018, pp. 2048–2085.
(with G. Avalos and P. G. Geredeli) Semigroup Well-posedness of A Linearized, Compressible Fluid with
An Elastic Boundary, Discrete Contin. Dyn. Syst. Ser. B, Volume 23, 3, 2018, pp.1267--1295.
(with J. Howell and I. Lasiecka) Quasi-stability and Exponential Attractors for A Non-Gradient
System---Applications to Piston-Theoretic Plates with Internal Damping, Evolution Equns. Control Theory,
Volume 5, 4, 2016, pp. 567--603.
(with G. Avalos and P.G. Geredeli) Finite Dimensional, Smooth Attractors for A Non-rotational Berger Plate
with Dissipation Acting on A Portion of the Boundary, Comm. Pure Appl. Analy.,
Volume 15, 6, 2016, pp. 2301--2328.
(with E. Dowell, I. Chueshov, and I. Lasiecka) Mathematical Aeroelasticity: A Survey,
Mathem. Engin. Sci. Aerosp., Volume 7, 2016, pp. 1--26.
(with E. Dowell, I. Chueshov, and I. Lasiecka) Nonlinear elastic plate in a flow of gas:
Recent results and conjectures, Appl. Math. Optim., Volume 73, 2016, pp. 475--500.
(with L. Bociu, G. Guidoboni, R. Sacco) Analysis of nonlinear poro-elastic and poro-visco-elastic models,
Arch. Rational Mech. Anal., Volume 222, 3, pp. 1445--1519.
(with P. G. Geredeli) Qualitative Results on the Dynamics of A Berger Plate with
Nonlinear Boundary Damping, Nonlin. Anal. B, 31, 2016, pp. 227--256.
(with I. Lasiecka) Feedback stabilization of a fluttering panel in an inviscid
subsonic potential flow, SIAM J. Math. Anal., 48, 3, 2016, pp. 1848--1891.
(with M. Peszynska and R.E. Showalter) Advection of methane in the hydrate zone:
Model, analysis, and examples, Math. Meth. Appl. Sci., Volume 38, 18, 2015, pp. 4613--4629.
(with I. Lasiecka) Eliminating flutter in clamped von Karman plates
immersed in subsonic flows, Comm. Pure Appl. Anal., Volume 13, 5, 2014, pp. 1935--1969.
(with I. Lasiecka) Kutta-Joukowski flow conditions in flow-plate interactions: subsonic case,
Nonlinear Anal. B, Volume 7, 2014, pp. 171--191.
(with I. Chueshov and I. Lasiecka) Flow-plate interactions: Well-posedness and long-time behavior,
Discrete Contin. Dyn. Syst. Ser. S, Spec. Vol.: New Developments in Mathematical Theory of Fluid Mech. ,
Volume 7, 5, 2014, pp. 925--965.
(with P. G. Geredeli) Decay rates to equilibrium for nonlinear plate equations with geometrically constrained,
degenerate dissipation, Appl. Math. Optim. , Volume 68, 2013, pp. 361--390.
(with I. Chueshov and I. Lasiecka) Attractors for delayed, non-rotational von Karman plates
with applications to flow-structure interactions without any damping,
Comm. PDE Volume 39, 11, 2014.
(with I. Chueshov and I. Lasiecka) Evolution semigroups in supersonic flow-plate interactions,
J. Diff. Equns. Volume 254, Issue 4, 2013, pp. 1741--1773.
(with P. G. Geredeli and I. Lasiecka) Smooth attractors of finite dimension for von Karman evolutions
with nonlinear frictional damping localized in a boundary layer,
J. Diff. Equns. Volume 254, Issue 3, 2013, pp. 1193--1229.
(with I. Lasiecka) Generation of bounded semigroups in nonlinear subsonic flow-structure interactions
with boundary dissipation, Math. Meth. Appl. Sci., Volume 36, 2013, pp. 1995--2010.
Weak and strong solutions of a nonlinear subsonic flow-structure interaction: Semigroup approach,
Nonlinear Anal. A, Volume 74, Issue 10, July 2011, pp. 3123--3136.
(with D. P. Sheehan and L. M. Baird) Orthogonally-oriented nanotube arrays: Experiment I,
J. Nanosci. Nanontech., Volume 7, Issue 10, 2007, pp. 3653--3661.
Proceedings and Surveys
(with I. Lasiecka and I. Chueshov) Nonlinear Flow-Structure Interaction: A Survey,
Nonlinear World Journal of Inter-disciplinary Nature, 1(1), December 2017, pp. 31–-50.
(with I. Lasiecka) Stabilization of a nonlinear flow-plate interaction via component-wise decomposition,
XV International Conference on Hyperbolic Problems: Theory, Numerics, Applications, July 2014,
IMPA, Rio de Janeiro, Brazil, Bull. Braz. Math. Soc., New Series 47(2), 2016, pp. 489--506.(peer-reviewed)
(with I. Lasiecka) Controlling Flutter for Nonlinear Panels in Subsonic Flows via
Nonlinear Mechanical Feedback, IEEE 53rd Conference on Decision and Control,
Session on Control of First and Second Order PDEs, 2014, pp. 577--582.(peer-reviewed)
(with I. Lasiecka) Long-time dynamics and control of subsonic flow-structure interactions,
American Control Conference (ACC), 2012, pp. 658--663, 27-29 June 2012. (peer-reviewed)