# Dr Nikos Kavallaris

Nikos graduated from University of Athens with a BSc degree in Mathematics in 1994. He received MSc in Pure Mathematics from University of Athens in 1996 and his PhD from National Technical University of Athens in 2000. He joined the Department of Mathematics of University of Chester in September 2013.

## Qualifications

B.Sc. M.Sc. PhD.

## Overview

Before joining the University of Chester, Nikos spent 1 year lecturing Engineering Mathematics to Rochester Institute of Technology (RIT) Dubai Campus, UAE where he had a position as an Assistant Professor. Before joining RIT-Dubai, Nikos spent 5 years at Aegean University, Greece, as an Assistant Professor.

In the period 2004 -2005 Nikos held a research position in the University of Wroclaw, in the framework of HYKE (Hyperbolic Kinetic Equations) EU funded research project. Later, from 2005-2006 he received a scholarship for the Greek National Scholarships Foundation of Greece (I.K.Y) for postdoctoral research at the National Technical University of Athens. Afterwards, in the period 2006-2007 he worked as a postdoctoral researcher in a project founded by Centre of Excellence (COE) program of Japanese Government at Osaka University, Japan.

Previously, he has worked as a Visiting Lecturer at the National Technical University of Athens for 3 years (2001-2004) lecturing Mathematics to Mechanical, Civil, Chemical and Electrical Engineering students.

Nikos had a full scholarship during his PhD studies in the National Technical University of Athens from 1997 to 2000. Moreover he achieved several research projects among which was an EU Marie-Curie project.

Nikos has presented part of his research participating in several international conferences.

- Shortcuts
- Teaching
- Research
- Published Work

## Teaching

Nikos has been provisionally assigned MA 4001 (Mathematical & Numerical Methods), MA 4006 (Finite Mathematics), MA 5006 (Probability Theory and Statistical Methods), MA 6004 (Differential Equations & Mathematical Modelling) and MA 7008 (Differential Equations & Their Applications) .

During his time in RIT-Dubai, Nikos taught Pre-calculus, Calculus I,II, Engineering, Multivariable Calculus, Probability and Statistics for Engineers and Differential Equations .While at Aegean University, he taught many courses like First and Second Year Calculus, Linear Algebra, Differential Equations, Real Analysis. During his time as a Visiting Lecturer in National Technical University he taught many courses among which Mathematical Modelling and Asymptotic Analysis, Ordinary and Partial Differential Equations, Theory of Dynamical Systems, Engineering Calculus, Numerical Analysis for PDE’s, Application of MATHEMATICA and MATLAB in the solution of Mathematical and Physical problems.

## Research

Nikos is researching in the area of Nonlinear Partial Differential Equations and Reaction Diffusion-Systems . His research focuses on

- Mathematical Analysis of Nonlinear Ordinary and Partial Differential Equations (Investigation of Blow-up and Quenching phenomena).
- Qualitative Analysis of Reaction-Diffusion Systems arising in Mathematical Biology and Ecology.
- Mathematical Modelling in MEMS technology, Cell dynamics, and Ohmic Heating process.
- Mathematical Analysis of Stochastic Partial Differential Equations (Regularity of solutions and investigation of singular phenomena like Blow-up).

**Research grants **

- London Mathematical Society, Scheme 4 Grant, March 2014, (Budget: £702- Ref No. 41335).
- (2010-2014) EU Marie-Curie International Exchange Staff Exchange Scheme, Project title: “Mathematical studies on critical nonequilibrium phenomena via mean field theories and theories of nonlinear partial differential equations". Aegean University Coordinator. (Budget: 105,840 €)
- (1/1/2011-31/12/2012) PEVE. Funded by National Technical University of Athens. Project: “Mathematical Modelling and Analysis of Problems arise in Porous media, Microelectromechanical Systems, Chemotaxis and Marine Ecology”. Held by Professor D.E. Tzanetis. (Budget: 15,000 €)
- (4/2006-8/2007). Japanese Ministry of Education funded Project entitled “The 21st COE(Center Of Excellence) Program Towards a New Basic Science: Depth and Synthesis”, held by Professor T. Suzuki. (Budget: 2,000,000 ¥)

## Published work

- (A.A. Lacey, C.V. Nikolopoulos and D.E. Tzanetis) ‘’On the quenching behaviour of some semilinear wave equation arising in MEMS technology”, Discrete and Continuous Dynamical System- A, Volume 35, Number 3, March 2015, 1009–1037doi:10.3934/dcds.2015.35.1009.

- (with M. Al-Refai ) “On Computation of bounds of the bifurcation parameter for a non-local elliptic equation with increasing non-linearity”, Computers and Mathematics with Applications, Volume 66, Issue 4, September 2013, Pages 512–524

- (with T. Suzuki) “Non-local reaction–diffusion system involving reaction radius II: rate of convergence”, IMA Journal of Applied Mathematics, (2012), 1-21 doi:10.1093/imamat/hxs032

- (with J-S. Guo) “Non-local reaction-diffusion system involved by reaction radius I”, IMA Journal of Applied Mathematics, (2012), 1−19 doi:10.1093/imamat/hxr068 (joined with T. Suzuki).

- “On a non-local parabolic problem arising in electrostatic MEMS control”, Discrete and Continuous Dynamical Systems-A., (2012), 32, 1723-1746.

- (with M. Al-Refai and M. Ali Hajji ) “Monotone Iterative Sequences for Non-local Elliptic Problems”, European Journal of Applied Mathematics vol. 22, (2011), pp. 533–552

- (with A.A. Lacey, C.V. Nikolopoulos and D.E. Tzanetis) “A hyperbolic nonlocal problem modelling MEMS technology”, Rocky Mountain Journal of Mathematics, Vol 41, (2011) no 2, 505-534

- (with T. Suzuki) “An analytic approach to the normalized Ricci flow-like equation”, Nonlinear Analysis: Theory Methods and Applications Vol 72 (2010), no. 5, 2300-2317

- (with Ph. Souplet) “Grow-up rate and refined asymptotics for a Patlak-Keller-Segel model in a disk”, SIAM Journal on Mathematical Analysis, Vol 40 (2008/09), no. 5, 1852—1881,

- (with T. Miyasita and T. Suzuki ) “Touchdown and related problems in electrostatic, MEMS device equation”, Nonlinear Differential Equations and Applications, 15 (2008), 363-385,

- (with A.A. Lacey, C.V. Nikolopoulos and C. Voong) “Behaviour of a non-local equation modelling linear friction welding”, IMA Journal of Applied Mathematics,. Vol 72, No 5, (2007), 597 – 616

- ( with A.A. Lacey, C.V. Nikolopoulos and D.E. Tzanetis) “Asymptotic analysis and estimates of blow-up time for the radial symmetric semilinear heat equation in the open-spectrum case”, Mathematical Methods in Applied Sciences., Vol 30, No 13, (2007) , 1507 – 1526

- (with T. Suzuki) “On the finite-time blow-up of a non-local parabolic equation describing chemotaxis”, Differential and Integral Equations, Vol 20, No. 3, (2007), 293 – 308,

- (with T. Nadzieja) “On the blow-up of the non-local thermistor problem”, Proceedings of the Edinburgh Mathematical Society, Vol 49, (2007) , 1-21.

- (with M. Al-Refai ) “Bounds and critical parameters for a class of non-local problems”, Electr. Journ. Diff. Equations, Vol 2006 No.29 (2006), 1-16.

- (D.E. Tzanetis) “On the blow-up of a non-local parabolic problem”, Applied Mathematics Letters, 16 (2006), 921 – 925

- (with D.E. Tzanetis) “Behaviour of a non-local convective problem with variable velocity in Ohmic heating process”, Banach Center Publications, 66 (2004) 189 - 198.

- (with V. Zisis). “The Dual Integral Equation Method in Hydromechanical Systems”, Journal of Applied Mathematics , 6 (2004) 447 – 460,

- “Asymptotic behaviour and blow-up for a nonlinear diffusion problem with a non-local source term”, Proceedings of the Edinburgh Mathematical Society (2004) 47, 375 - 395.

- (with A.A. Lacey and D.E. Tzanetis) “Global existence and divergence of critical solutions of some non-local parabolic problems in Ohmic heating process”, Nonlinear Analysis: Theory Methods and Applications, 58 (2004) 787-812.

- (with D.E. Tzanetis) “An Ohmic heating non-local diffusion-convection problem for the Heaviside function”, Australian and New Zealand Industrial and Applied Mathematics Journal (Electronic Version), (2002), pp. E114-E142.

- (with D.E. Tzanetis) “Behaviour of critical solutions of a non-local hyperbolic problem in Ohmic heating of foods”, Applied Mathematics E-Notes, 2(2002), 59-65.

- (with C.V. Nikolopoulos and D.E. Tzanetis) “Estimates of blow-up time for a non-local problem modelling an Ohmic heating process”, European Journal of Applied Mathematics, (2002), Vol. 13 pp. 337-351

- (With D.E. Tzanetis) “Blow-up and stability of a non-local diffusion-convection problem arising in Ohmic heating of foods”, Differential and Integral Equations, Vol. 15, N. 3, (2002), 271-288