RIT on Applied PDE Archives for Fall 2024 to Spring 2025
Organizational meeting
When: Mon, September 9, 2024 - 3:00pmWhere: Kirwan Hall 1311
Speaker: () -
Introduction to kinetic theory, part 1
When: Mon, September 16, 2024 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Dave Levermore (UMD) -
Introduction to kinetic theory, part 2
When: Mon, September 23, 2024 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Dave Levermore (UMD) -
An introduction to coupled fluid-structure dynamics
When: Mon, September 30, 2024 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Jeffrey Kuan (UMD) -
Quasilinear Parabolic-Hyperbolic Systems from the Mechanics of Solids.
When: Mon, October 21, 2024 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Stuart Antman (UMD) -
Abstract:
Soliton dynamics for classical scalar fields
When: Mon, October 28, 2024 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Andrew Lawrie (UMD) -
Abstract: I will present an introduction to some of my work with Jacek Jendrej. We study classical scalar fields in dimension 1+1 with a symmetric double-well self-interaction potential. Examples of such equations are the phi-4 model and the sine-Gordon equation. These nonlinear wave equations admit non-trivial static solutions called kinks and antikinks, which are amongst the simplest examples of topological solitons. We define an n-kink cluster to be a solution approaching, for large positive times, a superposition of n alternating kinks and antikinks whose velocities converge to zero and mutual distances grow to infinity. Our main result is a determination of the leading order asymptotic behavior of any n-kink cluster. We use this information to construct the n-dimensional invariant manifold of n-kink clusters, which plays the dynamical role of the stable/unstable manifold for an ideal "critical point at infinity” given by well separated multi-kink configurations. In this context we also explain the role of kink clusters as universal profiles for the formation/annihilation of multikink configurations.
Discrete coagulation-fragmentation in the critical case.
When: Mon, November 4, 2024 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Jiwoong Jang (UMD) -
Abstract: In this talk, we present a discrete coagulation-fragmentation equation when the two effects are balanced. A Hamilton-Jacobi equation is derived through the Bernstein transform. By analyzing this equation together with a power series, we discuss the existence and uniqueness of mass-conserving solutions to the coagulation-fragmentation equation according to the initial mass. Large-time behavior and equilibria of the discrete model are also discussed, which exhibits different phenomena from the continuous model. This is joint work with Hung V. Tran.
A proof of Vishik's nonuniqueness theorem for the forced 2D Euler equation
When: Mon, November 18, 2024 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Seyed Abdolhamid Banihashemi (UMD) -
Hele-Shaw flow with surface tension and kinetic undercooling as a singular limit of the fully parabolic Keller-Segel system with nonlinear diffusion.
When: Mon, December 2, 2024 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Michael Rozowski (UMD) -
Organizational meeting
When: Mon, February 3, 2025 - 3:00pmWhere: Kirwan Hall 1311
Speaker: () -
Introduction to velocity averaging
When: Mon, February 10, 2025 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Dave Levermore (UMD) -
Dirichlet to Neumann map
When: Mon, February 17, 2025 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Bowen Chen (UMD) -
Anomalous Dissipation in Bounded Domains
When: Mon, March 10, 2025 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Ethan Dudley (UMD) -
Sharp interface limits of some models of chemotaxis
When: Mon, March 24, 2025 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Michael Rozowski (UMD) -
Abstract: We will review some models of chemotaxis featuring some mechanisms that prevent overcrowding. These are variants of classical Patlak-Keller-Segel systems that model the population density of some organisms who follow a chemical signal that they themselves produce. Then, we will describe some recent results by Antoine Mellet, Inwon Kim, Yijing Wu, Jeremy Sheung-Him Wu, and myself that show, in a singular limit formally corresponding to that of a large population, that the organisms arrange themselves into a region of constant positive density. Finally, we derive mean-curvature-driven free boundary problems describing the evolution of the boundary of this region, which allows to understand the migration of the population in the limit.
The coupled dynamics of compressible fluids interacting with elastic structures
When: Mon, March 31, 2025 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Jeffrey Kuan (UMD) -
Pseudodifferential operators and applications to the Landau magnetic Laplacian
When: Mon, April 7, 2025 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Ben Goldschlager (UMD) -
The FBI transform and its applications, I
When: Mon, April 14, 2025 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Shiferaw Berhanu (UMD) -
Abstract: In these two lectures, we will introduce a class of non-
linear transforms called the FBI transforms (after Fourier, Bros,
and Iagolitzner) that characterize local and microlocal regularity
of functions (and distributions) in C^{\infty}, real analytic, and Gevrey
spaces. If time permits, we will present applications to linear and
nonlinear pdes with complex-valued coefficients.
On the Nonlinear Instabililty of the Euler Equations
When: Mon, April 21, 2025 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Sepehr Mohammadkhani (UMD) -
The FBI transform and its applications, II
When: Mon, April 28, 2025 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Shif Berhanu (UMD) -
Abstract: Abstract. In these two lectures, we will introduce a class of non-
linear transforms called the FBI transforms (after Fourier, Bros,
and Iagolitzner) that characterize local and microlocal regularity
of functions (and distributions) in C∞, real analytic, and Gevrey
spaces. If time permits, we will present applications to linear and
nonlinear pdes with complex-valued coefficients.
The FBI transform and applications, III
When: Mon, May 5, 2025 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Shif Berhanu (UMD) -
Lᵖ-based (1 < p < +∞) regularity of the tangent Stokes equations on Cᵏ (k ≥ 2) closed manifolds
When: Mon, May 12, 2025 - 3:00pmWhere: Kirwan Hall 1311
Speaker: Gonzalo Benavides (UMD) -