SEMINAR “Contemporary Analysis and Partial Differential Equations” (23.03.2023)





Eugene Benilov

University of Limerick, Ireland

Solitary and Periodic Waves in a Fifth-Order Korteweg-de Vries Equation

Thursday, 23 March 2023 at 15:00

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I consider a fifth-order KdV equation, where the fifth-order derivative term is multiplied by a small parameter ε. It has been conjectured that this equation admits a non-local solitary wave solution which has a central core and an oscillatory tail either behind or in front of the core. I shall prove that this solution cannot be exactly steady; instead, the amplitude of the central core decays due to the energy flux generated in the oscillatory tail. The decay rate is calculated in the limit ε → 0. In order to verify the analytical results, I have developed a high-precision spectral method for numerical integration of this equation. The asymptotic and numerical result show good agreement.

SEMINAR “Contemporary Analysis and Partial Differential Equations” (24.02.2023)





Marina Chugunova

Claremont Graduate University

Mathematical Modeling of Pressure Regimes in Fontan Blood Flow Circulation

Friday, 24 February 2023 at 18:00

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Babies born with a single functioning heart ventricle instead of the usual two require a series of surgeries during the first few years of life to redirect their blood flow. The resulting circulation, in which systemic venous blood flows directly into the pulmonary arteries, bypassing the heart, is referred to as the Fontan circulation. We develop two mathematical lumped parameter models for blood pressure distribution in the Fontan blood flow circulation: an ODE based spatially homogeneous model and a PDE based spatially inhomogeneous model. Numerical simulations of the ODE model with physiologically consistent input parameters and cardiac cycle pressure-volume outputs reveal the existence of a critical value for pulmonary resistance above which the cardiac output dramatically decreases. Joint work with: M.G. Doyle, J.P. Keener, S.L. Roche and R.M. Taranets.

Seminar video report

SEMINAR “Contemporary Analysis and Partial Differential Equations” (24.01.2023)





Georgy Kitavtsev

Middle East Technical University, Northern Cyprus Campus

Liquid crystal defects in the Landau–de Gennes theory of liquid crystals

Tuesday, 24 January 2023 at 12:00

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In this talk I will introduce and motivate Q-tensors and the associated Landau–de Gennes energy modelling liquid crystal configurations not far from the thermodynamic equilibrium. İmposing k-radially symmetric boundary conditions I will show that the critical points consistent with the symmetry of the boundary conditions exist only in the case k=2 and identify three types of radial profiles: with two, three or full five components and numerically investigate their minimality and stability properties depending on suitable parameters. Generic bifurcation diagrams for different type solutions are then calculated numerically and justified analytically. This is a joint work with Valeriy Slastikov and Jonathan Robbins (University of Bristol) and Arghir Zarnescu (Basque Center for Applied Mathematics).


Seminar video report