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Dario Valdebenito, Ph.D.

Dr. Valdebenito was born and raised in Chile, and earned a B.S. in Mathematical Engineering, and a diploma in Mathematical Engineering, from the University of Chile. Afterwards, he earned a M.Sc. and Ph.D. in Mathematics from the University of Minnesota. After postdoctoral work at McMaster University (Hamilton, Ontario, Canada) and the University of Tennessee (Knoxville, TN, U.S.A.), he joined ɫ��ӰƬ as an assistant professor of mathematics.

In addition to his research experience, Dr. Valdebenito has taught mathematics at a college level for over 15 years, in a variety of educational settings (large and small classes, in person and online, in Spanish and English...), and strives to serve both the mathematical community (via peer-reviews, authoring reports for Mathematical Reviews) and the community at large.

Beyond mathematics, Dr. Valdebenito studied music for many years, plays the piano and has some basic singing skills. Dr. Valdebenito was a member of the tenor section of the Twin Cities Catholic Chorale, as well as of the schola at the Church of St. Agnes (St. Paul, MN), and the schola at Holy Ghost Church (Knoxville, TN). Beyond any formal studies, Dr. Valdebenito is interested in opera, the arts, history, planes, trains, and automobiles.

Dr. Valdebenito's research is focused on partial differential equations. Most of his research has revolved around spatial dynamics, in which elliptic equations (which are time-independent) are analyzed using techniques from dynamical systems (which are usually employed to study time-dependent equations). Recent research is concerned with studying the behavior of fluids with very low viscosity near the boundary, relative to the behavior of ideal fluids (with no viscosity), the so-called boundary layer problem.

• Phan, T., and D. Valdebenito. “A Boundary Layer Problem in Domains with Non-Flat Boundaries with Measurable Viscous Coefficients.” Studies in Applied Mathematics 1-30, 2022.
• Valdebenito, D. “On Solutions Arising from Radial Spatial Dynamics of Some Semilinear Elliptic Equations.” 2021 UNC Greensboro PDE Conference. Electronic Journal of Differential Equations, Conf. 26 (2022): 151-69.
• Polacik, P., and D. Valdebenito. “Further Results on Quasiperiodic Partially Localized Solutions of Homogeneous Elliptic Equations on R^(N+1).” Journal of Functional Analysis 282, no. 12 (2022), article no.  109457.
• Polacik, P., and D. Valdebenito. “The Existence of Partially Localized Periodic-Quasiperiodic Solutions and Related KAM-Type Results for Elliptic Equations on the Entire Space.” Journal of Dynamics and Differential Equations 34 (2021): 3035-56.
• Polacik, P., and D. Valdebenito. “Existence of Partially Localized Quasiperiodic Solutions of Homogeneous Elliptic Equations on R^(N+1).” Annali della Scuola Normale Superiore di Pisa—Classe di Scienze 21 (2020): 771-800.
• Polacik, P., and D. Valdebenito. “Existence of Quasiperiodic Solutions of Elliptic Equations on the Entire Space with a Quadratic Nonlinearity.” Discrete and Continuous Dynamical Systems, Series S 13, no. 4 (2019): 1369–93.
• Polacik, P., and D. Valdebenito. “Some Generic Properties of Schrodinger Operators with Radial Potentials.” Proceedings of the Royal Society of Edinburgh 149A (2019): 1435-51.
• Polacik, P., and D. Valdebenito. “Existence of Quasiperiodic Solutions of Elliptic Equations on R^(N+1) via Center Manifold and KAM Theorems.” Journal of Differential Equations 262 (2017): 6109-64.
• Felmer, P., and D. Valdebenito. “Eigenvalues for Radially Symmetric Fully Nonlinear Singular or Degenerate Operators.” Nonlinear Analysis: Theory, Methods and Applications 75 (2012): 6524-40.