Partial Differential Equations and Analysis Seminar

The partial differential equations and analysis seminar is the research seminar associated with the applied and nonlinear analysis, and the analysis and geometry programs.

No events are currently scheduled.

Past events

24
Sep
2019

On $L_2$-uniqueness of symmetric diffusion equations »
We discuss the uniqueness of solutions of the parabolic evolution equation $\partial\varphi/\partial t+H\varphi=0$ where $H=-\mathrm{div}(C\nabla)$ is a second-order degenerate elliptic operator acting on a domain $\Omega$ in $\mathbf{R}^d$.
17
Sep
2019

Riesz transforms on a class of non-doubling manifolds II »
We consider L^p boundedness of the Riesz transform on a class of non-doubling manifolds obtained by taking the connected sum of two Riemannian manifolds which are both a product of a Euclidean space and a closed manifold.
27
Aug
2019

Special Lagrangian equations & Optimal transport for dendritic structures »
In this seminar, Professor Yu Yuan and Professor Young-Heon Kim will discuss special lagrangian equations and optimal transport for dendritic structures.
27
Aug
2019

Special Lagrangian equations & Optimal transport for dendritic structures »
In this seminar, Professor Yu Yuan and Professor Young-Heon Kim will discuss special lagrangian equations and optimal transport for dendritic structures.
16
Aug
2019

Geometry of Ricci solitons »
In this seminar, Professor Huai-Dong Cao will discuss some recent progress on Ricci solitons, especially in dimension four.
13
Aug
2019

A new phenomenon involving inverse curvature flows in hyperbolic space »
In this seminar, we discover a new phenomenon involving inverse curvature flows in hyperbolic space.
09
Aug
2019

Dynamics of a Fisher-KPP nonlocal diffusion model with free boundaries »
Professor Yihong Du will introduce and discuss a class of free boundary problems with "nonlocal diffusion".
06
Aug
2019

Energy critical 2-D stochastic wave equation »
In this seminar, Nimit Rana will prove the existence and uniqueness of a local maximal solution to a $H^1$-critical stochastic wave equation with multiplicative noise on a smooth bounded domain $\mathcal{D} \subset \mathbb{R}^2$ with exponential nonlinearity.
09
Jul
2019

The perfectly matched layer (PML): theory and practice »
In this talk we discuss the well-posedness and stability of the PML initial boundary value problem. In particular, we will perform a spectral analysis of the integro-differential operator corresponding to the PML-IBVP, and derive general solutions of the PML-IBVP in the Fourier- Laplace domain.
11
Jun
2019

Bounds on the maximal Bochner-Riesz means for elliptic operators »
I will discuss $L^p$ boundedness of the maximal Bochner-Riesz means for self-adjoint operators of elliptic type which satisfy  the finite speed of propagation for the associated wave operator.
04
Jun
2019

Weyl Pseudodifferential Operators in Ornstein-Uhlenbeck Settings »
The classical Weyl pseudodifferential calculus is a particular choice of "quantisation". Ornstein-Uhlenbeck (OU) operators are analogs of the Laplacian adapted to spaces with Gaussian measure. I will explain my current work in adapting the Weyl calculus to the OU setting.
28
May
2019

On square functions in the control of linear systems »
I will survey some fundamental concepts in linear systems.
17
May
2019

Disclinations in 3D Landau-de Gennes theory »
In this talk I will introduce a new bifurcation theory to find multiple solutions of Landau-de Gennes equation.
14
May
2019

Spaces of functions invariant under Fourier integral operators of order zero (part 2) »
This talk follows up on the seminar by Andrew Hassell on May 8. However, at the start of my talk I will recall the contents of his seminar, so that the talk is accessible without prior knowledge of the subject.
07
May
2019

Spaces of functions invariant under Fourier integral operators of order zero »
It was proved by Seeger, Sogge and Stein that Fourier Integral operators (FIOs) in $n$ dimensions map the Hardy space $H^1$ into $L^1$ provided they have sufficiently negative order, that is, no bigger than $-(n-1)/2$.

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