Členovia výskumného tímu z KAMŠ

• prof. RNDr. Marek Fila, DrSc. ✟
• prof. RNDr. Pavol Quittner, DrSc.
• Mgr. Petra Macková

Výskum je zameraný na štúdium vlastností riešení nelineárnych difúznych rovníc a systémov, ako aj úloh s nelineárnymi a dynamickými okrajovými podmienkami. Okrem otázok spojených s existenciou a jednoznačnosťou sú vyšetrované najmä asymptotické vlastnosti riešení.

Výber publikácií

1. M. Fila, J. L. Vázquez, M. Winkler, E. Yanagida: Rate of convergence to Barenblatt profiles for the fast diffusion equation, Archive Rational Mech. Anal. 204 (2012), 599-625.
2. M. Fila, M. Winkler: Rate of convergence to separable solutions of the fast diffusion equation, Israel J. Math. 213 (2016).
3. M. Fila, M. Winkler: Optimal rates of convergence to the singular Barenblatt profile for the fast diffusion equation, Proc. Royal Soc. Edinburgh A 146 (2016), 309-324.
4. M. Fila, K. Ishige, T. Kawakami: Minimal solutions of a semilinear elliptic equation with a dynamical boundary condition, J. Math. Pures Appl. 105 (2016), 788-809.
5. M. Fila, M. Winkler: Slow growth of solutions of superfast diffusion equations with unbounded initial data, J. London Math. Soc. 95 (2017), 659-683.
6. M. Fila, M. Winkler: A Gagliardo-Nirenberg-type inequality and its applications to decay estimates for solutions of a degenerate parabolic equation, Adv. Math. 357 (2019), Art. No. 106823.
7. T. Bartsch, P. Poláčik, P. Quittner: Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations, J. European Math. Soc. 13 (2011), 219-247.
8. P. Quittner, Ph. Souplet: Symmetry of components for semilinear elliptic systems, SIAM J. Math. Anal. 44 (2012), 2545-2559.
9. P. Quittner: Liouville theorems for scaling invariant superlinear parabolic problems with gradient structure, Math. Ann. 364 (2016), 269-292.
10. P. Quittner, Ph. Souplet: Superlinear Parabolic Problems. Blow-up, Global Existence and Steady States, Birkhäuser Advanced Texts, Birkhäuser, Cham 2019, Second (revised and expanded) edition.