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Dr. Paschalis Karageorgis

Assistant Professor (Pure & Applied Mathematics)

  Mathematical analysis   Pure mathematics
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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
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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, ACCEPTED
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, PUBLISHED
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, PUBLISHED
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, PUBLISHED
Paschalis Karageorgis, Dispersion relation for water waves with non-constant vorticity , European Journal of Mechanics - B/Fluids, 34, 2012, p7 - 12, Journal Article, IN_PRESS  TARA - Full Text
Paschalis Karageorgis, Asymptotic expansion of radial solutions for supercritical biharmonic equations , Nonlinear Differential Equations and Applications, 19, (4), 2012, p401 - 415, Journal Article, PUBLISHED
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, PUBLISHED
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, PUBLISHED
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, PUBLISHED  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, PUBLISHED  TARA - Full Text

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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.