Publications

[60] K. Fellner, J. Fischer, M. Kniely, B.Q. Tang, Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion, preprint

[59] K. Fellner, C. Muench, On hysteresis-reaction-diffusion systems: singular fast-reaction limit derivation and nonlinear hysteresis feedback, preprint.

[58] K. Fellner, M. Kniely, Uniform convergence to equilibrium for a family of drift-diffusion models with trap-assisted recombination and self-consistent potential, open access Math. Methods Appl. Sci., 44 no.17 (2021) 13040—13059.

[57] K. Fellner, J. Morgan, B.Q. Tang, Uniform-in-time bounds for quadratic reaction-diffusion systems with mass dissipation in higher dimensions, Discrete and Continuous Dynamical Systems - Series S, 14 no.2 (2021) 635—651.

[56] K. Fellner, M. Kniely, Uniform convergence to equilibrium for a family of drift-diffusion models with trap-assisted recombination and the limiting Shockley-Read-Hall model, open access Journal of Elliptic and Parabolic Equations, 6 no.2 (2020) 529—598.

[55] K. Fellner, E. Latos, B.Q. Tang, Global regularity and convergence to equilibrium of reaction-diffusion systems with nonlinear diffusion, open access Journal of Evolution Equations, 20 no.3 (2020) 957—1003.

[54] K. Fellner, B. Hughes, Solutions of a non-local aggregation equation: universal bounds, concavity changes and efficient numerical solutions, open access Math. Methods Appl. Sci., 43 no.8 (2020) 5398—5429.

[53] K. Fellner, J. Morgan, B.Q. Tang, Global classical solutions to quadratic systems with mass control in arbitrary dimensions, Annales Institute H. Poincaré (C) Anal. Non Linéaire, 37 no.2 (2020) 281—307.

[52] M. Brokate, K. Fellner, M. Lang-Batsching, Weak differentiability of the control-to-state mapping in a parabolic problem with hysteresis, NoDEA, 26 no.6 (2019).

[51] K. Fellner, E. Latos, T. Suzuki, Large-time asymptotics of a public goods game model with diffusion, open access Monatshefte für Mathematik, 190 no.1 (2019) 101—121.

[50] M. Doumic, K. Fellner, M. Mezache, H. Rezaei, A bi-monomeric nonlinear Becker-Döring-type system to capture oscillatory aggregation kinetics in prion dynamics, Journal of Theoretical Biology, 480 (2019) 241—261.

[49] K. Fellner, S. Sonner, B.Q. Tang, D.D. Thuan, Stabilisation by noise on the boundary for a Chafee-Infante equation with dynamical boundary conditions, Discrete and Continuous Dynamical Systems - Series B, 24 no.8 (2019) 4055—4078.

[48] K. Baur, K. Fellner, M.J. Parsons, M. Tschabold, Growth behaviour of periodic tame friezes, Revista Matemática Iberoamericana, 35 no. 2 (2019) 575—606.

[47] H. Egger, K. Fellner, J.-F. Pietschmann, B.Q. Tang, Analysis and Numerical Solution of Coupled Volume-Surface Reaction-Diffusion Systems with Application to Cell Biology, Applied Mathematics and Computation, 336 (2018) 351—367.

[46] K. Fellner, B.Q. Tang, Convergence to equilibrium of renormalised solutions to nonlinear chemical reaction-diffusion systems, open access in ZAMP, 69 (2018) first online article 54.

[45] K. Fellner, E. Latos, B.Q. Tang, Well-posedness and exponential equilibration of a volume-surface reaction-diffusion system with nonlinear boundary coupling, Annales Institute H. Poincaré (C) Anal. Non Linéaire, 35 no.3 (2018) 643—673.

[44] K. Fellner, M. Kniely, On the entropy method and exponential convergence to equilibrium for a recombination-drift-diffusion system with self-consistent potential, Applied Mathematics Letters, 79 (2018) 196—204.

[43] L. Desvillettes, K. Fellner, B.Q. Tang, Trend to equilibrium for reaction-diffusion systems arising from complex balanced chemical reaction networks, SIAM Journal on Math. Analysis, 49 no.4 (2017) 2666—2709.

[42Proc] K. Fellner, B.Q. Tang, Entropy methods and convergence to equilibrium for volume-surface reaction-diffusion systems, From Particle Systems to Partial Differential Equations, PSPDE IV, Braga, Portugal, December 2015, Springer Proceedings in Mathematics and Statistics (2017) 153—176.

[41] M. Breden, L. Desvillettes, K. Fellner, Smoothness of moments of the solutions of discrete coagulation equations with diffusion, open access in Monatshefte für Mathematik, 183 no.3 (2017) 437—463.

[40] K. Fellner, B.Q. Tang, Explicit exponential convergence to equilibrium for nonlinear reaction-diffusion systems with detailed balance condition, DOI, Nonlinear Analysis, 159 (2017) 145—180.

[39] K. Fellner, W. Prager, B.Q. Tang, The entropy method for reaction-diffusion systems without detailed balance: first order chemical reaction networks, Kinetic and Related Models., 10 no.4 (2017) 1055—1087.

[38] K. Fellner, E. Latos, T. Suzuki, Global classical solutions for mass-conserving, (super)-quadratic reaction-diffusion systems in three and higher space dimensions, Discrete and Continuous Dynamical Systems - Series B, 21 no.10, (2016) 3441—3462.

[37] K. Fellner, V. Kovtunenko, A discontinuous Poisson--Boltzmann equation with interfacial transfer: homogenisation and residual error estimate, open access in Applicable Analysis, 95 no. 12 (2016) 2661—2682.

[36] K. Fellner, E.-H. Laamri, Exponential decay towards equilibrium and global classical solutions for nonlinear reaction-diffusion systems, Journal of Evolution Equations, 16 no. 3 (2016) 681—704.

[35] K. Fellner, S. Rosenberger, B.Q. Tang, Quasi-Steady-State Approximation and Numerical Simulation for a Volume-Surface Reaction-Diffusion System., Communications in Mathematical Sciences, 14 no. 6 (2016) 1553—1580.

[34IMN] K. Baur, K. Fellner, Mathematics and Arts: Towards a balance between artistic intuition and mathematical complexity, International Mathematical News of the Austrian Mathematical Society, 231 (2016) 1—14.

[33] K. Fellner, V. Kovtunenko, A singularly perturbed nonlinear Poisson--Boltzmann equation: uniform and super-asymptotic expansions, Mathematical Methods in the Applied Sciences, 38 no. 16 (2015) 3575—3586.

[32] L. Desvillettes, K. Fellner, Duality- and Entropy Methods for Reversible Reaction-Diffusion Equations with Degenerate Diffusion, Mathematical Methods in the Applied Sciences, 38 no. 16 (2015) 3432—3443.

[31] K. Fellner, E. Latos, G. Pisante, On finite time blow-up for filtration problem with nonlinear reaction, Applied Mathematics Letters, 42 (2015) 47—52.

[30Proc] L. Desvillettes, K. Fellner, Exponential Convergence to Equilibrium for a Nonlinear Reaction-Diffusion Systems Arising in Reversible Chemistry, System Modelling and Optimization, IFIP AICT, 443 (2014) 96—104.

[29] J.A. Canizo, L. Desvillettes, K. Fellner, Improved duality estimates and applications to reaction-diffusion equations, Comm. Partial Differential Equations, 39 no.6 (2014) 1185—1204.

[28] L. Desvillettes, K. Fellner, Duality- and Entropy Methods in Coagulation-Fragmentation Models, Revista di Matematica della Universita di Parma, 4 no.2 (2013) 215—263.

[27] B. Hughes, K. Fellner, Continuum models of cohesice stochastic swarms: the effect of motility on aggregation patterns, Physica D, 260 (2013) 26—48.

[26] D. Brinkman, K. Fellner, P. Markowich, M.-T. Wolfram , A Drift-Diffusion-Reaction Model for Excitonic Photovoltaic Bilayers: Asymptotic Analysis and a 2-D HDG Finite Element Scheme, Math. Models and Methods in Applied Sciences, 23 (2013) 839—872.

[25] E. Hackett-Jones, K. Landman, K. Fellner, Aggregation patterns from non-local interactions: discrete stochatic and continuum modelling, Physical Review E 85 (2012) 041912.

[24] A. Chertock, K. Fellner, A. Kurganov, A. Lorz, P. Markowich, Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach, Journal of Fluid Mechanics 694 (2012) 155—190.

[23] K. Fellner, G. Raoul, Stability of stationary states of non-local interaction equations, Mathematical and Computer Modelling 53 (2011) 1436—1450.

[22] K. Fellner, G. Raoul, Stable stationary states of non-local interaction equations, Mathematical Models and Methods in Applied Sciences 20 (2010) 2267—2291.

[21Proc] J.A. Canizo, L. Desvillettes, K. Fellner, Absence of Gelation for Models of Coagulation-Fragmentation with Degenerate Diffusion, Il Nuovo Cimento, Proceedings of the ICTT 33 (2010) 79—86.  

[20Proc] L. Desvillettes, K. Fellner, Methods for Reaction-Diffusion Equations with Degenerate Diffusion Arising in Reversible Chemistry, accepted in the probably never to be printed Proceedings of the Equadiff 2007.

[19] R. Duan, K. Fellner, Ch. Zhu, Energy Method for Multi-dimensional Balance Laws with Non-local Dissipation, J. Math. Pures Appl. 93 (2010) 572—598.

[18] J.A. Canizo, L. Desvillettes, K. Fellner, Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion, Annales Institute H. Poincaré (C) Anal. Non Linéaire 27 (2010) 639—654.

[17] L. Desvillettes, K. Fellner, Large time asymptotics for a Continuous Coagulation-Fragmentation Model with Degenerate Size-dependent Diffusion, SIAM J. Math. Anal. 41 (2009) 2315—2334.

[16] J. Carrillo, L. Desvillettes, K. Fellner, Rigorous Derivation of a Nonlinear Diffusion Equation as Fast-Reaction Limit of a continuous Coagulation--Fragmentation Model with Diffusion, Comm. Partial Differential Equations 34 (2009) 1338—1351.

[15] M. Di Francesco, K. Fellner, P. Markowich, The entropy dissipation method for inhomogeneous reaction--diffusion systems, Proc. Royal Soc. A 464 (2008) 3272—3300.

[14] L. Desvillettes, K. Fellner, Entropy Methods for Reaction-Diffusion Equations: Slowly Growing A-priori Bounds, Revista Matemática Iberoamericana. 24 no. 2 (2008) 407—431.

[13] M. Di Francesco, K. Fellner, H. Liu, A non-local conservation law with nonlinear ‘radiation’ inhomogeneity, JHDE 5 no. 1 (2008) 1—23.

[12] J. Carrillo, L. Desvillettes, K. Fellner, Fast-Reaction Limit for the Inhomogeneous Aizenman-Bak Model. Kinetic and Related Models 1 no.1 (2008) 127—137.

[11] J. Carrillo, L. Desvillettes, K. Fellner, Exponential Decay Towards Equilibrium for the Inhomogeneous Aizenman-Bak Model. Comm. Math. Physics. 278 no. 2 (2008) 433—451.

[10Proc] L. Desvillettes, K. Fellner, Entropy Methods for Reaction-Diffusion Equations: Degenerate Diffusion. DCDS Supplements Special (2007) 304—312.

[9] K. Fellner, C. Schmeiser, Classification of equilibrium solutions of the cometary flow equation and explicit solutions of the Euler equations for monatomic ideal gases. J. Stat. Phys. 129 no.3 (2007) 493—507.

[8] L. Desvillettes, K. Fellner, M. Pierre, J. Vovelle, About Global Existence for Quadratic Systems of Reaction-Diffusion, Advanced Nonlinear Studies 7 no.3 (2007) 491—511.

[7Proc] K. Fellner, V. Miljanovic, C. Schmeiser, Entropy Method for the Linearized Cometary Flow Equation, Proceedings of the Tenth International Conference on Hyperbolic Problems I, Editors F. Asakura, S. Kawashima, A Matsumura, S. Nishibata, K. Nishihara, ISBN 4-946552-21-9, Yokohama Publishers (2006).

[6] K. Fellner, V. Miljanovic, C. Schmeiser, Convergence to equilibrium for the linearised cometary flow equation, Trans. Theory Stat. Phys. 35 no.3-4 (2006) 109—136.

[5] L. Desvillettes, K. Fellner, Exponential Decay toward Equilibrium via Entropy Methods for Reaction-Diffusion Equations, JMAA 319 no. 1 (2006) 157—176.

[4] J. Carrillo, K. Fellner, Long-time Asymptotics via Entropy Methods for Diffusion Dominated Equations, Asymptotic Analysis 42 no.1-2 (2005) 29—54.

[3] K. Fellner, C. Schmeiser, Burgers-Poisson: a nonlinear dispersive model equation. SIAM J. Appl. Math. 64 no.5 (2004) 1509—1525 (electronic).

[2] K. Fellner, L. Neumann, C. Schmeiser, Convergence to global equilibrium for spatially inhomogeneous kinetic models of non-micro-reversible processes, Monatsh. Math. 141 no. 4 (2004) 289—299.

[1] K. Fellner, F. Poupaud, C. Schmeiser, Existence and convergence to equilibrium of a kinetic model for cometary flows, J. Stat. Phys. 114 no. 5-6 (2004) 1481—1499.

[PhD-thesis] K. Fellner, On two models for charged particle systems: The cometary flow equation and the Burgers-Poisson system.