## About Dr Nikos Kavallaris

Before joining the University of Chester, Nikos spent spent 5 years at Aegean University, Greece, initially as an Assistant Professor and later as Associate 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.

### Awards-Scholarships

- Papakyriakopoulos Foundation: Doctoral scholarship (1/09/1997- 31/3/2000).

- National Scholarships Foundation of Greece: Postdoctoral scholarship (1/1/2005- 31/3/2006).

- Hyperbolic Kinetic Equations (HYKE) European Training Program: Postdoctoral scholarship, Wroclaw University, Poland, October 2004–May 2005.

- IBM Fellowship ($ 5, 000), June-July 2018, Department of Applied Mathematics, Brown University.

### Miscellaneous Academic Activities

- Member of the Editorial Board for the scientific journal
**PLOS ONE**. - Member of the London Mathematical Society
- Reviewer for the American Mathematical Society
- External Examiner for Undergraduate and Postgraduate Programmes on Applied Mathematics forXi’an Jiaotong – Liverpool University (in China) (Academic Years: 2017–18, 2018–19, 2019–2020, 2020–21).
- . Member of the London Mathematical Society (LMS) Library Committee.

## 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

### Research grants

- (3/2004 – 8/2006). Greek Ministry of Education funded project “Pythagoras I” entitled “Dynamicsof Infinite-Dimensional Discrete and Continuum Dynamical Systems” held by Prof. N.M. Stavrakakis and Prof. D. E. Tzanetis (National Technical University of Athens-NTUA, Greece)(Budget: Euros 115,000).

- (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: Euros 105,840).
- (6/2005 – 11/2007). Greek Ministry of Education funded Project “Pythagoras II” entitled “Mathematical Analysis of Wave Propagation in Chiral Media” held by Prof. A. Athanasiadis (Budget: Euros 90,000).

- (6/2003–11/ 2004). Greek Ministry of Education funded project “Thalis I” entitled “MathematicalAnalysis of some Nonlinear Differential Equations” held by Prof. D. E. Tzanetis (National Technical University of Athens-NTUA, Greece) in collaboration with Prof. A.A. Lacey (Heriot-Watt University,Scotland). (Budget: Euros 60,000).

- (1/1/2011-31/12/2012) PEVE. Funded by National Technical University of Athens. Project: “MathematicalModelling and Analysis of Problems arise in Porous media, Microelectromechanical Systems,Chemotaxis and Marine Ecology”. Collaboration with Professor D.E. Tzanetis. (Budget: Euros 30,000).

- (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: Yen 2,000,000 )

- London Mathematical Society, Scheme 4 Grant, March 2014, (Budget: £702- Ref No. 41335). The budgetwas used to support the research visit of my collaborator Prof. Michael Winkler in the Department of Mathematics of University of Chester.

- London Mathematical Society, Scheme 1 Grant, July 2015, (Budget: £600- Ref No. 11473). The budget was used to support part of the organization expenses of the workshop “Mathematical and Computational Modelling of Biological Systems” which took place in Thornton Science Park of University of Chester on 23rd of September 2015.

- International Research Excellence Awards (2017–18) funded by Santander, (Budget: £2,340). The budgetwill be used to support the research visit of my collaborator Dr. Anastasios Matzavinos from BrownUniversity to the Department of Mathematics of University of Chester during the academic year 2017–18.

### Research Interests

1. Deterministic and Stochastic Modelling of phenomena arising in Biology (Chemotaxis, Angiogenesis, Tumour Growth, DNA Methylation, Cell motility e.t.c ), Ecology (Mutualism), Game Theory (Replicator Dynamics) as well as of Industrial processes (Ohmic Heating, Resistance Spot Welding, Linear Friction Welding in Metals, Torsion Test in Metals, MEMS control e.t.c. ).

2. Mathematical Analysis of Nonlinear and Non-local Parabolic Deterministic & Stochastic Differential Equations and Reaction Diffusion Systems

3. Uncertainty Quantification of stochastic models arising in Biology, Ecology, Finance, etc.

## Published Work

- N.I. Kavallaris, Quenching solutions of a stochastic parabolic problem arising in electrostatic MEMS control,
**Math. Meth. Appl. Sci., Vol.****41****(****2018****)****1074****–****1082****DOI:****10****.****1002****/mma.****4176****.** - N. I. Kavallaris, T. Ricciardi and G. Zecca, A multi-species chemotaxis system: Lyapunov functionals, duality, critical mass,
**European Journal of Applied Mathematics doi:****10****.****1017****/S****0956792517000286****,****(****2017****), pp.****1****–****28****.** - N. I. Kavallaris and T. Suzuki, On the dynamics of a non-local parabolic equation arising from the Gierer-Meinhardt system,
**Nonlinearity****30****(****2017****)****1734****–****1761****.** - N.I. Kavallaris J. Lankeit and M. Winkler, On a degenerate nonlocal parabolic problem describing infinite dimensional replicator dynamics,
**SIAM Journal of Mathematical Analysis Vol****49****(****2017****), no.****2****,****954****–****983****.** - N.I. Kavallaris, A.A. Lacey and C.V. Nikolopoulos, On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control,
**Nonlinear Analysis: Theory Methods and Applications Vol****138****no.****5****, (****2016****),****189****–****206****, Nonlinear Partial Differential Equations, (invited paper for special****volume in honor of Juan Luis Vázquez for his****70****th birthday doi:****10****.****1016****/j.na.****2016****.****02****.****001****).** - N.I. Kavallaris, Explosive solutions of a stochastic non-local reaction–diffusion equation arising in shear band formation,
**Mathematical Methods in the Applied Sciences, Vol.****38****, (****2015****),****3564****–****3574****,****DOI:****10****.****1002****/mma.****3514****.** - N.I. Kavallaris and Y. Yan, A Time Discretization Scheme for a Nonlocal Degenerate Problem Modelling Resistance Spot Welding,
**Mathematical Modelling of Natural Phenomena Vol.****10****, No.****6****, (****2015****),****91****–****113****, DOI:****10****.****1051****/mmnp/****201510308****(invited paper on the special volume entitled: “Nonlocal****reaction-diffusion equations”)** - N.I. Kavallaris, 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 SystemsA, Volume****35****, Number****3****, (****2015****),****1009****–****1037****doi:****10****.****3934****/dcds.****2015****.****35****.****1009****.** - N. Kavallaris and T. Suzuki, The normalized Ricci flow-like equation: revisited,
**Applied Mathematics Letters Volume****44****, (****2015****),****30****–****33****.** - N. Kavallaris and T. Suzuki, Nonlocal reaction-diffusion system involved by reaction radius II: Rate of convergence,
**IMA J Appl Math (****2014****)****79****(****1****):****1****–****21****doi:****10****.****1093****/imamat/hxs****032****.** - M. Al-Refai and N.I. Kavallaris, 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****, (****2013****),****512****–****524****.** - N.I. Kavallaris and T. Suzuki, Non-local reaction-diffusion system involved by reaction radius I,
**IMA J Appl Math (****2013****)****78****(****3****):****614****–****632****.** - J-S. Guo and N.I. Kavallaris On a non-local parabolic problem arising in electrostatic MEMS control,
**Discrete and Continuous Dynamical Systems-A., (****2012****),****32****,****1723****–****1746****.** - M. Al-Refai, N.I. Kavallaris and M. Ali Hajji, Monotone Iterative Sequences for Non-local Elliptic Problems,
**European Journal of Applied Mathematics vol.****22****, (****2011****), pp.****533****–****552****.** - N.I. Kavallaris, 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****,****(invited paper for a special volume in honor of Jerrold Bebernes for his****70****th birthday).** - N.I. Kavallaris and 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****.** - N.I. Kavallaris and 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****.** - N.I. Kavallaris, T. Miyasita and T. Suzuki, Touchdown and related problems in electrostatic, MEMS device equation,
**Nonlinear Differential Equations and Applications,****15****(****2008****),****363****–****385****.** - N.I. Kavallaris, 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****.** - N.I. Kavallaris, 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****.** - N.I. Kavallaris and 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****.** - N.I. Kavallaris and T. Nadzieja, On the blow-up of the non-local thermistor problem,
**Proceedings of the Edinburgh Mathematical Society, Vol****49****, (****2007****) ,****1****–****21****.** - M. Al-Refai and N.I. Kavallaris, Bounds and critical parameters for a class of non-local problems,
**Electr. Journ. Diff. Equations, Vol****2006****No.****29****(****2006****),****1****–****16****.** - N.I. Kavallaris and D.E. Tzanetis, On the blow-up of a non-local parabolic problem,
**Applied Mathematics Letters,****16****(****2006****),****921****–****925****.** - N.I. Kavallaris and D.E. Tzanetis, Behaviour of a non-local convective problem with variable velocity in Ohmic heating process,
**Banach Center Publications,****66****(****2004****)****189****–****198****.** - N.I. Kavallaris and V. Zisis, The Dual Integral Equation Method in Hydromechanical Systems,
**Journal of Applied Mathematics,****6****(****2004****)****447****–****460****.** - N.I. Kavallaris, 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****.** - N.I. Kavallaris, 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****.** - N.I. Kavallaris and 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. E****114****–E****142****.** - N.I. Kavallaris and 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****.** - N.I. Kavallaris, 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****.** - N.I. Kavallaris and 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****, No.****3****, (****2002****),****271****–****288****.**

### Books

Title:**“Non-Local Partial Differential Equations for Engineering and Biology: Mathematical Modeling and Analysis”**

Series: **Mathematics for Industry**

Editor: **Springer**

Status: **Published in December ****2017**

## Qualifications

B.Sc. M.Sc. PhD.