# Karlstad Applied Analysis Symposia and Lectures (KAASL)

KAASL is a series of mini-courses and mini-symposia in pure and applied mathematics.

## NEXT EVENTS

**When:** September 9th, 10:00-11:30**What:** On Moser’s iteration technique as applied to PDEs**Who:** Vishnu Raveendran (Karlstad)**Where:** https://kau-se.zoom.us/j/61589448054

**Abstract:** The main aim of the presentation is to see the application of Moser Iteration technique used in Partial Differential Equations. We divide the discussion into three parts. In the first part we demonstrate the application of Moser Iteration in a simple elliptic equation defined on a bounded domain *U* , to obtain the control of L-infinity norm of solution on a smaller domain by L^{2} norm of solution in *U*. In the second part we redo the same estimate for a parabolic setting. In the last part, we quickly discuss some recent results obtained from Moser Iteration technique.

## PREVIOUS EVENTS

**When:** May 26**What:** Reading club: Mean-field Games**Who:** Toyohiko Aiki**Where:** https://kau-se.zoom.us/j/61738267378

**When:** May 19**What:** Reading club: Mean-field Games**Who:** Adrian Muntean**Where:** https://kau-se.zoom.us/j/61738267378

**When:** May 14**What:** Reading club: Mean-field Games**Who:** Omar Richardson**Where:** https://kau-se.zoom.us/j/61738267378

**When:** October 29, 11:00-12:30**What:** Reading club: Heterogeneous multiscale methods**Who:** Omar Richardson (KAU)**Where:** Mathematics Library (21F5)

**When:** October 18, 13:00-14:30**What:** Reading club: Heterogeneous multiscale methods**Who:** Adrian Muntean (KAU)**Where:** Mathematics Library (21F5)

**When:** October 14, 13:00-14:30**What:** Reading club: Heterogeneous multiscale methods**Who:** Adrian Muntean (KAU)**Where:** Mathematics Library (21F5)

**When:** October 9, 08:30-10:00**What:** Reading club: Heterogeneous multiscale methods**Who:** Omar Richardson (KAU)**Where:** Mathematics Library (21F5)

**When:** March 28, 13:15-14:00**What:** Geometry in the Dark Ages: From Isidore of Seville (c. 560-636) to Nicole Oresme (1320-1382)**Who:** Bogdan Suceava, State University of California at Fullerton, USA**Where:** 21E202

Abstract: Isidore’s Etymologies enjoyed a wide audience during the medieval period. We investigate the structure of mathematics, as it is described in the Etymologies, and we discuss the sources on which Isidore relied when he described the structure of mathematics. A change of paradigm took place in Europe after the Recovery of Aristotle, in later centuries. It is quite surprising that the concept of curvature appears for the first time in the monograph De configurationibus, written by Nicole Oresme around 1350. We describe this work and its historical context, as well as further implications of Oresme’s “doctrine of configurations”, written by an author that, very likely, did not use Euclid’s Elements among his sources.

The visit of Prof. Suceava is partially founded by the Wenner-Gren Foundation.

**When:** March 13, 9:15**What:** Asymptotic analysis of an $\varepsilon$-Stokes problem with Dirichlet boundary conditions**Who:** Kazunori Matsui, Kanazawa University, Japan**Where:** Mathematics library

In this talk, we present an $\varepsilon$-Stokes problem connecting the classical Stokes problem and the corresponding pressure-Poisson equation using one parameter $\varepsilon>0$. We prove that the solution to the $\varepsilon$-Stokes problem convergences as $\varepsilon$ tends to 0 or $\infty$ to the classical Stokes or pressure-Poisson problem, respectively. Numerical results illustrate the expected behavior of the weak solutions.

This work is supervised by Profs. Masato Kimura (Kanazawa) and Adrian Muntean (Karlstad) and is done with the support of our STINT project: “Mathematics Bachelor Program for Efficient Computations” (contract nr. DD2017-6936).

**When:** February 13, 10:15**What:** Introductory Talk on Inverse Problems**Who:** Simon Grützner, University of Bremen, Germany**Where:** Mathematics library

**Abstract:** A typical field for applying the theory of Inverse Problems is the one of parameter identification, where one aims to identify a material parameter from an experimentally obtained data set, for example. Real measurements always output noisy data, so that some question arise quiet naturally: Is it even possible to obtain the true parameter out of noisy data? How does the noise level effect the identification process?

The aim of this talk is not to answer these questions in general, but rather to shed some light on these via simple examples and to explain some of the main concepts of the theory of Inverse Problems and their connection to the aforementioned questions.

**When:** October 25, 15:15**What:** Some results on interacting diffusions approximating the porous medium equation and propagation of chaos**Who:** Thieu Thi Kim Thoa, University of L’Aquila, Italy **Where:** Mathematics library

**Abstract:** Some results on interacting diffusions approximating the porous medium equation and propagation of chaos in the paper of Robert Philipowski will be presented. The aims of this paper are to study a system of interacting diffusions and to show that for a large number of particles its empirical measure approximates the solution of the porous medium equation.

**When:** October 12, 15:00**What:** Reading club "Harmonic Analysis and PDE"**Who:** Adrian Muntean**Where:** Mathematics library

**Abstract:** The general aim of these regular one hour meetings is to understand some connections between harmonic analysis and partial differential equations. We will use the lecture notes for Klainerman's Princeton graduate course as starting point.

The reading club starts off on August 30. We will normally meet on Wednesdays afternoon (modulo the KAAS events).

For more information, contact Prof. A. Muntean.

References:

[1] S. Klainerman, lecture notes, 2008, Princeton University

**When:** March 15, 9:00**What:** Mini-course: "An overview on Fluctuation-Dissipation Theorems"**Who:** Matteo Colangeli, University of L’Aquila, Italy **Where:** Math. library floor 5**Abstract:** We discuss the foundations of the Fluctuation-Dissipation theorem, which allows to connect the response of a system to an external perturbation with the fluctuations characterizing the unperturbed dynamics. We will review the original Green-Kubo Formulae, the Kramers-Kronig relations and also discuss some applications to stochastic dynamics described by a Langevin equation and the extension to chaotic dissipative systems, cf. Refs. [1-5].

References:

[1] Kubo R., Statistical--mechanical theory of irreversible processes: I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Japan 12, 570 (1957).

[2] Marini B., Marconi U., Puglisi A., Rondoni L. and Vulpiani A., Fluctuation-dissipation: response theory in statistical physics, Phys. Rep. 461, 111 (2008).

[3] Colangeli M., Maes C. and Wynants B., A meaningful expansion around detailed balance, J. Phys. A: Math. Theor. 44, 095001 (2011).

[4] Lucarini V. and Colangeli M., Beyond the linear fluctuation-dissipation theorem: the role of causality, J. Stat. Mech.: Theor. Exp. P05013 (2012).

[5] Colangeli M., Rondoni L. and Vulpiani A., Fluctuation-dissipation relation for chaotic non-Hamiltonian systems, J. Stat. Mech.: Theor. Exp. L04002 (2012).