I study systems of partial differential equations where interaction elicits compelling phenomena. Dynamic coupling may create instability, transmit dissipation, destroy regularity, or trigger resonances.    Research    CV    Google Scholar    Email    Collaboration Tree

In my room, the world is beyond my understanding /
But when I walk, I see that it consists of three or four hills and a cloud. - WALLACE STEVENS

I am a Professor of Mathematics and the Undergraduate Program Director in the Department of Mathematics and Statistics at UMBC. My research analyzes models and develops frameworks for coupled PDE systems. This work touches on mathematical aeroelasticity, fluid-structure interactions, stability and periodicity in partially dissipative systems, and poroelastic and filtration dynamics. I teach throughout the undergraduate and graduate mathematics curriculum, mentor students and early-career researchers, and work on curriculum, enrollment/recruitment, and outreach.

Faculty e-mail: websterj@umbc.edu

Undergraduate Program Director e-mail: mathstatupd@umbc.edu

Phone (Office): 410/455-2183

Office: MP430

Department: Department of Mathematics and Statistics, UMBC

Mailing Address: UMBC, 1000 Hilltop Circle, Baltimore, MD 21250

Profiles: Google Scholar, ResearchGate, LinkedIn

Mathematical aeroelasticity and self-destabilizing systems

Flutter, post-flutter dynamics, stabilization, attractors, and nonconservative coupling in nonlinear flow-structure systems.

Partial dissipation, stability, periodicity, and resonance

Semigroup, resolvent, and spectral methods for decay, periodic solvability, regularity loss, and resonance in coupled evolution equations.

Modern analytical poroelasticity

Nonlinear, degenerate, inertial, and reduced-dimensional Biot systems, together with poroelastic structures and fluid-poroelastic interaction.

From polynomial stability to periodic well-posedness in partially dissipative systems (with P. Galdi and B. Muha, 2026). This work extends the stability-to-periodicity principle to a heretofore intermediate regime: polynomially stability. Partially dissipative systems with this property are shown to have periodic well-posedness, explicitly quantifying the temporal regularity loss required for periodic solvability.

Weak Solutions and Inertial Limits for Quasi-static Filtrations (with P. Lavagnino and A. Lee, 2026). This paper develops weak solutions for inertial and quasi-static filtration models and rigorously analyzes the singular limit connecting the two regimes. We produce a novel existence result for quasi-static Stokes-Biot dynamics.

Steady Weak Solutions for a Plate Coupled to Compressible Viscous Flow with Inflow-Outflow Boundary Conditions (with B. Muha, Š. Nečasová, M. Pokorný, and S. Trifunović, 2026).

This work constructs steady weak solutions for a nonlinear plate coupled to compressible viscous flow with inflow and outflow. This paper extends stationary flow-structure analysis to an open-flow configuration with an undetermined (variable) boundary.

Time-Periodic Solutions for Hyperbolic-Parabolic Systems (with S. Mosný, B. Muha, and S. Schwarzacher), accepted in the Journal of the European Mathematical Society, 2026. The paper establishes periodic solvability for a broad class of coupled hyperbolic-parabolic (heat-wave) systems by obtaining observability type estimates.

PDE Control: From Classical to Emerging Themes and Methods, Research in the Mathematical Sciences, 2025. This co-edited special collection surveys classical foundations and emerging directions in the analysis and control of partial differential equations.

Flutter Stabilization for an Unstable, Hyperbolic Flow-Plate Interaction (with I. Lasiecka), in Fluids under Control, Birkhäuser, 2024. This chapter develops a component-wise stabilization strategy for a flow-plate system whose coupling can, in principle, generate flutter.

Mathematical Theory of Flow/Fluid-Structure Interactions, Oberwolfach Seminars, Springer, 2018. This collaborative volume develops analytical foundations for several major classes of fluid-structure interaction models.

2023 GRIT-X lecture. A short public lecture on mathematical modeling, aeroelastic flutter, and the use of flow-induced oscillations in energy-harvesting applications.

UMBC article on flutter    NSF collaborative award    The Conversation: The invisible power of flutter

As an undergraduate program director at UMBC, I work on the undergraduate curriculum, mentor students, and engage in sustained partnerships with the Ingenuity Project of Baltimore City. These efforts connect UMBC mathematics and statistics with talented students in Baltimore City and support clearer pathways into mathematical study.

UMBC-Ingenuity Project partnership    Baltimore City outreach    Where are they now? UMBC students

My current NSF-supported project studies self-excitation, limit-cycle oscillations, and control in large-deflection structural models motivated by aeroelasticity and engineering applications.

Self-excitation, Limit Cycle Oscillations, and Control of Large Deflection Plate Models in Engineering Applications, NSF DMS-2307538 (2023-2027).