About

Irena Lasiecka is a Commonwealth Professor Emerita at the University of Virginia's Department of Mathematics. Her professional role is associated with the university's mathematics faculty, and she is recognized for her distinguished contributions to the field. Her contact information includes an email address (il2v@virginia.edu) and her office is located at 141 Cabell Drive, Kerchof Hall, Charlottesville, VA. The department highlights her as a notable member of the academic community, emphasizing her status as a professor emerita, which indicates her significant academic career and contributions to mathematics.

Research topics

• Mathematics
• Mathematical analysis
• Applied mathematics
• Physics
• Pure mathematics

Selected publications

• Large deflections of a flow-driven cantilever with Kutta-Joukowski flow conditions

  Discrete and Continuous Dynamical Systems - S · 2026-01-01

  articleOpen access

  We consider a canonical flow-structure system modeling airflow over a cantilevered beam. Flow-beam interactions arise in flight systems as well as alternative energy technologies, such as piezoelectric energy harvesters. A potential flow, given through a hyperbolic equation, captures the airflow interacting with a beam clamped on one end and free on the other. The dynamic coupling occurs through an impermeability condition across the beam; in the wake, the Kutta-Joukowski flow condition is imposed. Several challenges arise in the analysis, including the unboundedness of the flow domain, lack of interface trace regularity, and flow conditions giving rise to a dynamic and mixed boundary value problem. Additionally, we consider a recent nonlinear model capturing the cantilever large deflections through the effects of inextensibility. We produce a viable underlying semigroup for the model's linearization, which includes a flow regularity theory. Then, exploiting higher regularity nonlinear estimates for the beam, we utilize a semigroup perturbation to obtain local-in-time strong solutions for the nonlinear dynamics.

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• Stability and Gevrey regularity of the semigroup associated with an Euler–Bernoulli plate equation subject to localized Kelvin–Voigt damping

  Journal of Evolution Equations · 2026-01-19

  articleOpen access1st authorCorresponding

  Abstract We consider an Euler–Bernoulli plate equation with Kelvin–Voigt damping in a bounded domain. The damping is localized in an appropriate open strict subset $$\omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ω</mml:mi> </mml:math> of the domain $$\Omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Ω</mml:mi> </mml:math> . While it is known that the solutions of this model with a full damping $$\omega = \Omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ω</mml:mi> <mml:mo>=</mml:mo> <mml:mi>Ω</mml:mi> </mml:mrow> </mml:math> generate an analytic semigroup, this property is no longer valid for locally distributed damping. In view of this, we study regularity of the equation as expressed by a membership in an appropriate Gevrey’s class. It turns out that the final result depends on both “geometric” and analytical properties of the support function defining the dissipation. First, assuming that the damping coefficient d is $$C^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> and satisfies some structural conditions, we prove that the underlying semigroup is of Gevrey class s : for every $$s&gt;7/2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>7</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , when the damping region is a collar around the whole boundary, for every $$s&gt;4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> , when the damping region is more general, for every $$s&gt;7/2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>7</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , when the damping region is more general, and the function d is $$C^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:math> and satisfies one more structural condition than in the two cases above. In all cases, the semigroup is infinitely differentiable on $$(0,\infty )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>∞</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and also exponentially stable. Next, we drop the smoothness assumption on the damping coefficient and show that the corresponding semigroup decays at a rational rate $$O(t^{-1})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>t</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . Our proofs are based on the frequency domain method combined with an adequate smoothing procedure, interpolation inequalities, and multipliers technique. The main features of our proof of the Gevrey regularity are: (i) the introduction of suitable auxiliary functions, (ii) an appropriate estimate of the localized kinetic energy and exploitation of structural constraints on the damping coefficient to prove localized regularity, and, (iii) the use of Hahn–Banach theorem to derive a sharp estimate of a negative norm of the velocity nonsmooth component, (iv) the use of commutators to simplify our presentation. Our rational stability and Gevrey regularity results are the first for the plate equation with localized Kelvin–Voigt damping in higher space dimensions.

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• Uniform stabilization of the Boussinesq system in Besov spaces via finite dimensional, boundary-based fluid and interior thermal feedbacks

  Evolution equations and control theory · 2026-01-01

  articleOpen access1st authorCorresponding

  Let $ \Omega $ be an open, connected, bounded domain in $ \mathbb{R}^d, d = 2, 3, $ with boundary $ \Gamma = \partial \Omega $ of, say, class $ \mathrm{C}^2 $. Let $ \widetilde{\Gamma} $ be a connected, arbitrarily small portion of $ \Gamma $ and $ \omega $ be an arbitrarily small collar in $ \Omega $, supported by $ \widetilde{\Gamma} $ [Figure 2]. In $ \Omega $, we consider a Boussinesq system subject to a control triplet: $ \{\mathbf{{v}}, \mathbf{{u}}, g\} $. Here, $ \mathbf{{v}} $ is a localized boundary fluid control acting tangentially on $ \widetilde{\Gamma} $; $ \mathbf{{u}} $ is a localized interior fluid control acting tangentially in $ \omega $, i.e. in a direction parallel to $ \widetilde{\Gamma} $; and $ g $ is a localized interior thermal control acting on $ \omega $. The main result claims (well-posedness and) uniform feedback stabilization in the vicinity of an unstable stationary solution in a suitable Besov setting, depending on $ d $, of tight indices ('close to $ \mathrm{L}^3(\Omega) $ for $ d = 3 $), by means of explicitly constructed, localized, finite-dimensional, feedback controllers $ \{\mathbf{{v}}, \mathbf{{u}}, g\} $. Their dimension is the largest geometric multiplicity of the unstable eigenvalues. The Besov setting is by necessity; and so is the localizedinterior, tangential-like control $ \mathbf{{u}} $. The corresponding linear feedback problem defines a strongly continuous analytic semigroup, in fact of maximal regularity up to $ T = \infty $. This latter property is critically used in the analysis of well-posedness and uniform stabilization of the nonlinear feedback problem in the vicinity of an unstable equilibrium solution, as in [54] (Navier-Stokes boundary stabilization) or in [56] (Boussinesq stabilization with thermal boundary control). The 'ignition key' for the solutionof the corresponding linear global uniform stabilization problem is based on two unique continuation properties of suitably overdetermined adjointeigenproblems, one of which for the Boussinesq eigenproblem is proved [91] by Carleman-type estimates.

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• Numerical Approximation of Riccati-Based Hyperbolic-Like Feedback Controls

  Journal of Optimization Theory and Applications · 2025-03-27 · 1 citations

  articleOpen access1st authorCorresponding

  Abstract This paper provides a (rigorous) theoretical framework for the numerical approximation of Riccati-based feedback control problems of hyperbolic-like dynamics over a finite-time horizon, with emphasis on genuine unbounded control action. Both continuous and approximation theories are illustrated by specific canonical hyperbolic-like equations with boundary control, where the abstract assumptions are actually sharp regularity properties of the hyperbolic dynamics under discussion. Assumptions are divided in two groups. A first group of dynamical assumptions (actually dynamic properties) imply some preliminary critical properties of the control problem, including the definition of the would-be Riccati operator, in terms of the original data. However, in order to guarantee that such an operator is moreover the unique solution (within a specific class) of the corresponding Differential/Integral Riccati Equation, additional smoothing assumptions on the operators defining the performance index are required. The ultimate goal is to show that the the discrete finite dimensional Riccati based feedback operator, when inserted into the original PDE dynamics, provides near optimal performance.

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• Attractors for second order in time non-conservative dynamics with nonlinear damping

  Journal of Differential Equations · 2025-09-15

  article1st authorCorresponding
  PublisherDOI

• Sharp uniform stabilization of a shallow shell with internal rotational inertia dissipation and nonlinear boundary feedback under free boundary conditions

  Nonlinear Differential Equations and Applications NoDEA · 2025-06-26

  article1st authorCorresponding
  PublisherDOI

• Attractors For  Non-Conservative   Hyperbolic Like Dynamics with Nonlinear Damping Arising in Modeling Of  Plates Under Unstable Flow of Gas

  SSRN Electronic Journal · 2025-01-01

  preprintOpen access1st authorCorresponding
  PublisherDOI

• Stabilizing Energy-Critical Wave Equation to a Finite Dimensional Attractor via Nonlinear Damping

  ArXiv.org · 2025-10-20

  preprintOpen access1st authorCorresponding

  The wave equation with energy critical sources and nonlinear damping defined on a 3D bounded domain is considered. It is shown that the resulting dynamical system admits a global attractor. Under the additional assumption of strong monotonicity of the damping at the origin, it is shown that the originally unstable quintic wave is uniformly stabilised to a finite dimensional and smooth set. Moreover, the existence of exponential attractor is established. In order to handle \enquote{energy criticality} of both sources and damping, the methods used depend on enhanced dissipation \cite{Bociu-lasiecka-jde}, energy {\it identity} for weak solutions \cite{Koch-lasiecka}, an adaptation of Ball's method \cite{ball}, and the theory of quasi-stable systems \cite{chueshov-white}.

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• Sharp uniform stabilization of a shallow shell with internal rotational inertia dissipation and a nonlinear boundary feedback under free boundary conditions

  Research Square · 2025-01-01

  preprintOpen access1st authorCorresponding
  PublisherOA PDFDOI

• Attractors for Second Order in Time Non-Conservative Dynamics with Nonlinear Damping

  ArXiv.org · 2025-07-05

  articleOpen access1st authorCorresponding

  A long-time behavior of solutions to a nonlinear plate model subject to non-conservative and non-dissipative effects and nonlinear damping is considered. The model under study is a prototype for a suspension bridge under the effects of unstable flow of gas. To counteract the unwanted oscillations a damping mechanism of a nonlinear nature is applied. From the point of view of nonlinear PDEs, we are dealing with a non-dissipative and nonlinear second order in time dynamical system of hyperbolic nature subjected to nonlinear damping. One of the first goals is to establish ultimate dissipativity of all solutions, which will imply an existence of a weak attractor. The combined effects of non-dissipative forcing with nonlinear damping-leading to an overdamping-give rise to major challenges in proving an existence of an absorbing set. Known methods based on equipartition of the energy do not suffice. A rather general novel methodology based on ``barrier's'' method will be developed to address this and related problems. Ultimately, it will be shown that a weak attractor becomes strong, and the nonlinear PDE system has a coherent finite-dimensional asymptotic behavior.

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Recent grants

• Interface Control for Systems of Strongly Coupled Partial Differential Equations

  NSF · $329k · 2017–2021

• Control at the interface of strongly coupled partial differential equations

  NSF · $400k · 2013–2016

• Control Problems of Systems of Strongly Coupled Partial Differential Equations

  NSF · $304k · 1998–2002

• Control problems for systems of strongly coupled partial differential equations with variable coefficients.

  NSF · $476k · 2001–2006

• US-France Cooperative Research (INRIA): Control of Interactive Structures with Dynamic Shells

  NSF · $18k · 2003–2007

Frequent coauthors

• Roberto Triggiani

  University of Memphis

  201 shared

• Justin T. Webster

  72 shared

• Igor Čhuešhov

  52 shared

• George Avalos

  31 shared

• Francesca Bucci

  26 shared

• Jan Sokołowski

  Institut Élie Cartan de Lorraine

  25 shared

• Amjad Tuffaha

  20 shared

• Marcelo Bongarti

  Weierstrass Institute for Applied Analysis and Stochastics

  18 shared

Education

• Postdoctoral Fellow. , Systems Science Department

  University of California at Los Angeles

  1980

• PhD , Applied Mathematics

  University of Warsaw

  1975