Dionyssios Mantzavinos
University of Kansas, KS·Mathematics & Statistics
Waves in water and light pulses in optical fibers are described by partial differential equations (PDEs), equations that relate how a quantity changes in space and time. Real systems often have boundaries, such as a tank wall, a wavemaker or a fiber end, and these boundaries change how solutions behave in ways that are mathematically hard to handle.
- Fields
Mathematics & Statistics
Physics
- Topics
partial differential equations
nonlinear PDEs
integrable systems
- Grants
- 1 known grant, through Aug 2028
What they work on
- Develop analytical tools to establish existence, uniqueness and stability of solutions to nonlinear partial differential equations posed in bounded domains in two or more spatial dimensions.
- Analyze multi-component wave systems, where several interacting fields evolve together, under nonzero boundary conditions.
- Build a framework for wave equations with nonzero boundary conditions at infinity, connected to modulational instability and rogue waves.
More about the research
This project aims to build a general method for analyzing PDEs in bounded regions, in one and in several spatial dimensions.
Why it matters
Many wave equations studied here approximate the core equations of fluid motion, so the results could aid hydrodynamics and applied mathematics more broadly. The grant points to concrete uses in control theory, especially stabilization problems, in laboratory wave experiments such as the wavemaker problem, and in understanding rogue waves and modulational instability.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Mark Ablowitz
University of Colorado Boulder, CO·Mathematics & Statistics
Extend the Inverse Scattering Transform, which turns nonlinear wave equations into solvable linear scattering problems, to new classes of equations including fractional nonlinear wave equations with non-integer-order derivatives.
Camillo De Lellis
Princeton University, NJ·Mathematics & Statistics
Prove the existence of Navier-Stokes solutions whose kinetic energy dissipation stays positive as viscosity goes to zero, without adding spurious oscillations to the initial data, giving rigorous examples of anomalous dissipation.
Pablo Raúl Stinga
Iowa State University, IA·Mathematics & Statistics
Establish the analytical theory of surfaces of minimum mean curvature variation, smoothly bending surfaces used in data interpolation, image repair and hull design, including well-posedness and regularity of their equations.
The school
University of Kansas: 26 labs on PI Pages, $546M a year on research, 351 research doctorates a year.
Reach out
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