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Paschalis Karageorgis
Assistant Professor, Pure & Applied Mathematics

Publications and Further Research Outputs

Peer-Reviewed Publications

Marius Ghergu, Paschalis Karageorgis and Gurpreet Singh, Positive solutions for quasilinear elliptic inequalities and systems with nonlocal terms, Journal of Differential Equations, 268, (10), 2020, p6033 - 6066 Journal Article, 2020

Marius Ghergu, Paschalis Karageorgis and Gurpreet Singh, Quasilinear elliptic inequalities with Hardy potential and nonlocal terms, Proceedings A of the Royal Society of Edinburgh, 2020 Journal Article, 2020

Paschalis Karageorgis and Kimitoshi Tsutaya, On the asymptotic behavior of solutions of the wave equation of Hartree type, International Journal of Differential Equations and Applications, 16, (1), 2017, p11 - 44 Journal Article, 2017

Paschalis Karageorgis and Filippo Gazzola, Refined blow-up results for nonlinear fourth order differential equations, Communications on Pure and Applied Analysis, 14, (2), 2015, p677 - 693 Journal Article, 2015

Paschalis Karageorgis, Asymptotic expansion of radial solutions for supercritical biharmonic equations , Nonlinear Differential Equations and Applications, 19, (4), 2012, p401 - 415 Journal Article, 2012

Paschalis Karageorgis and John Stalker, A lower bound for the amplitude of traveling waves of suspension bridges, Nonlinear Analysis, 75, (13), 2012, p5212 - 5214 Journal Article, 2012

Paschalis Karageorgis, Dispersion relation for water waves with non-constant vorticity , European Journal of Mechanics - B/Fluids, 34, 2012, p7 - 12 Journal Article, 2012 TARA - Full Text

Elvise Berchio, Alberto Ferrero, Filippo Gazzola and Paschalis Karageorgis , Qualitative behavior of global solutions to some nonlinear fourth order differential equations , Journal of Differential Equations, 251, (10), 2011, p2696 - 2727 Journal Article, 2011

Paschalis Karageorgis, P.J. McKenna, Existence of ground states for fourth-order wave equations, Nonlinear Analysis: Theory, Methods & Applications, 73, (2), 2010, p367-373 Journal Article, 2010 TARA - Full Text

Alberto Ferrero and Hans-Christoph Grunau and Paschalis Karageorgis, Supercritical biharmonic equations with power-type nonlinearity, Annali di Matematica Pura ed Applicata, 188, (1), 2009, p171 - 185 Journal Article, 2009 TARA - Full Text

Paschalis Karageorgis, Stability and intersection properties of solutions to the nonlinear biharmonic equation, Nonlinearity, 22, (7), 2009, p1653 - 1661 Journal Article, 2009

Paschalis Karageorgis and John Stalker, Sharp bounds on 2m/r for static spherical objects, Classical and Quantum Gravity, 25, (19), 2008, p195021 (14 pp.) Journal Article, 2008

Paschalis Karageorgis and Walter A. Strauss, Instability of steady states for nonlinear wave and heat equations, Journal of Differential Equations, 241, (1), 2007, p184 - 205 Journal Article, 2007

Paschalis Karageorgis, Small-data scattering for nonlinear waves with potential and initial data of critical decay, Discrete and Continuous Dynamical Systems, 16, (1), 2006, p87 - 106 Journal Article, 2006

Paschalis Karageorgis and Kimitoshi Tsutaya, Small-data scattering for nonlinear waves of critical decay in two space dimensions, Differential and Integral Equations, 19, (6), 2006, p601 - 626 Journal Article, 2006

Paschalis Karageorgis and Kimitoshi Tsutaya, On the asymptotic behavior of nonlinear waves in the presence of a short-range potential, Manuscripta Mathematica, 119, (3), 2006, p323 - 345 Journal Article, 2006

Paschalis Karageorgis, Existence and blow up of small-amplitude nonlinear waves with a sign-changing potential, Journal of Differential Equations, 219, (2), 2005, p259 - 305 Journal Article, 2005

Research Expertise

Description

My research interests lie in the theory of nonlinear partial differential equations and I am particularly interested in equations that arise through mathematical physics. Starting with my PhD dissertation in 2004, I have worked on a variety of problems related to the heat, wave and biharmonic equations, the Vlasov-Einstein system from general relativity, some fourth-order models of suspension bridges and some elliptic inequalities involving the p-Laplace and mean curvature operators. In each case, my goal was to study the existence and qualitative properties of solutions such as decay, stability, scattering and asymptotic behaviour. Due to the wide range of problems that I have studied, the underlying techniques are inevitably diverse. To obtain sharp results for the wave equation, I had to improve some of the known space-time estimates. To study the static solutions of the Vlasov-Einstein system, I had to follow a dynamical systems approach. Some of my other papers used variational calculus to establish the existence of solutions for some elliptic equations, while some other papers used spectral analysis to study the (in)stability of static solutions. The main aspects in my research are diversity, generality and sharpness. First of all, I have managed to obtain results for a wide variety of problems including elliptic, parabolic and hyperbolic equations. In addition, most of my results are general in the sense that they apply to a wide range of equations under generic assumptions for the parameters involved. Most importantly, however, the vast majority of my results are known to be sharp. In other words, they establish conclusions under the best possible assumptions and they also illustrate that the conclusions are no longer valid, if any of the hypotheses are relaxed.

Keywords

Mathematical analysis; Pure mathematics

Recognition

Representations

Journal reviewer for: Discrete and Continuous Dynamical Systems

Journal reviewer for: Journal of Differential Equations

Journal reviewer for: Nonlinear analysis

Journal reviewer for: SIAM Journal of Mathematical Analysis