Preprints

• Cambi, A., Lidke, D.S., Ptashnyk, M., Smit, W., Sonner, S., Mathematical models for the EP2 and EP4 signaling pathways and their crosstalk, submitted (2025).
• Şen, Z., Sonner, S.,, Attractors for singular-degenerate porous medium type equations arising in models for biofilm growth, arXiv:2502.16649 (2025).
• Blessing, A., Seitz, T., Sonner, S., Tang, B. Q., Pathwise mild solutions for superlinear stochastic evolution equations and their attractors, arXiv:2502.01209 (2025).
• Smeets, R.K.H., Mitra, K., Pop, I.S., Sonner, S., Robust time-discretisation and linearisation schemes for singular and degenerate evolution systems modelling biofilm growth, arXiv:2404.00391 (2024).
• Mitra, K., Sonner, S., Well-posedness and qualitative properties of quasilinear degenerate evolution systems, arXiv:2304.00175 (2023).

Publications

• Lindemulder, N., Sonner, S., Cauchy problem for singular-degenerate porous medium type equations: well-posedness and Sobolev regularity, SIAM J. Math. Anal., to appear.
• Mitra, K., Hughes, J., Sonner, S., Eberl, H. J., Dockery, J., Travelling waves in a PDE–ODE coupled model of cellulolytic biofilms with nonlinear diffusion, J. Dynam. Differential Equations, 36 (2024), 3037-3071.
• Hughes, J., Sonner, S., Eberl, H. J., , A mathematical model of discrete attachment to a cellulolytic biofilm using random DEs, Math. Biosci. Eng. 19 (2022), 6582-6619.
• Hissink Muller, V., Sonner, S., Well-posedness of singular-degenerate porous medium type equations and application to biofilm models, J. Math. Anal. Appl. 509 (2022), paper no. 125894, 34 pp.
• Kuehn, C., Neamtu, A., Sonner, S., Random attractors via pathwise mild solutions for stochastic parabolic evolution equations, J. Evol. Equ. 21 (2021), 2631-2663.
• Rohanizadegan, Y., Sonner, S., Eberl, H. J., Discrete attachment to a cellulolytic biofilm modeled by an Itô stochastic differential equation, Math. Biosci. Eng. 17 (2020), 2236-2271.
• Han, X., Kloeden, P. E., Sonner, S., Discretisation of global attractors for lattice dynamical systems, J. Dynam. Differential Equations 32 (2020), 1457-1474.
• Hammami, M. A., Mchiri, L., Netchaoui, S., Sonner, S., Pullback exponential attractors for differential equations with variable delays, Discrete Contin. Dyn. Syst. Ser. B 25 (2020), 301-319.
• Fellner, K., Sonner, S., Thuan, D. D., Tang, B. Q., Stabilisation by noise on the boundary for a Chafee-Infante equation with dynamical boundary conditions, Discrete Contin. Dyn. Syst. Ser. B 24 (2019), 4055-4078.
• Ghasemi, M., Sonner, S., Eberl, H. J., Time adaptive numerical solution of a highly non-linear degenerate cross-diffusion system arising in multi-species biofilm modelling, European J. Appl. Math. 29 (2018), 1035-1061.
• Cresson, J., Sonner, S., A note on a derivation method for SDE models: applications in biology and viability criteria, Stoch. Anal. Appl. 36 (2018), 224-239.
• Hiremath, S. A., Surulescu, C., Zhigun, A., Sonner, S., On a coupled SDE-PDE system modeling acid-mediated tumor invasion, Discrete Contin. Dyn. Syst. Ser. B 23 (2018), 2339-2369.
• Caraballo, T., Sonner, S., Random pullback exponential attractors: general existence results for random dynamical systems in Banach spaces, Discrete Contin. Dyn. Syst. 37 (2017), 6383-6403.
• Emerenini, B. O., Sonner, S., Eberl, H. J., Mathematical analysis of a quorum-sensing induced biofilm dispersal model, Math. Biosci. Eng. 14 (2017), 625-653.
• Cresson, J., Puig, B., Sonner, S., Stochastic models in biology and the invariance problem, Discrete Contin. Dyn. Syst. Ser. B 21 (2016), 2145-2168.
• Kloeden, P. E., Sonner, S., Surulescu, C., A nonlocal sample dependence SDE-PDE system modeling proton dynamics in a tumor, Discrete Contin. Dyn. Syst. Ser. B 21 (2016), 2233-2254.
• Rahman, K. A., Sonner, S., Eberl, H. J., Derivation of a multi-species cross-diffusion model from a lattice differential equation and positivity of its solutions, Acta Physica Polonica B Proc. Suppl. (2016), 121-132.
• Sonner, S., Surulescu, C., Kloeden, P. E., Stochastic micro-macro models for acid mediated tumor invasion, YRS 2016 Proc., Fraunhofer Verlag (2016), 137-142.
• Kogoj, A. E., Sonner, S., Hardy inequalities for Δ_λ-Laplacians, Complex Var. Elliptic Equ. 61 (2016), 422-442.
• Sonner, S., Efendiev, M. A., Eberl, H. J., On the well-posedness of mathematical models for multicomponent biofilms, Math. Methods Appl. Sci. 38 (2015), 3753-3775.
• Sonner, S., Global attractors for semilinear parabolic problems involving X-elliptic operators, Bruno Pini Math. Anal. Semin., Univ. Bologna, Alma Mater Stud. (2015), 39-53.
• Kogoj, A. E., Sonner, S., Attractors met X-elliptic operators, J. Math. Anal. Appl. 420 (2014), 407-434.
• Carvalho, A. N., Sonner, S., Pullback exponential attractors for evolution processes in Banach spaces: properties and applications, Commun. Pure Appl. Anal. 13 (2014), 1141-1165.
• Sonner, S., A class of mathematical models describing processes in spatially heterogeneous biofilm communities, BIOMATH 2 (2013), 1312311, 10 p.
• Kogoj, A. E., Sonner, S., Attractors for a class of semilinear degenerate parabolic equations, J. Evol. Equ. 13 (2013), 675-691.
• Cresson, J., Puig, B., Sonner, S., Validating stochastic models: invariance criteria for systems of stochastic differential equations and the selection of a stochastic Hodgkin-Huxley type model, Internat. J. Biomath. Biostat. 2 (2013), 111-122.
• Carvalho, A. N., Sonner, S., Pullback exponential attractors for evolution processes in Banach spaces: theoretical results, Commun. Pure Appl. Anal. 12 (2013), 3047-3071.
• Cresson, J., Efendiev, M. A., Sonner, S., On the positivity of solutions of stochastic PDEs, ZAMM Z. Angew. Math. Mech. 93 (2013), 414-422.
• Sonner, S., Efendiev, M. A., Eberl, H. J., On the well-posedness of a mathematical model of quorum-sensing in patchy biofilm communities, Math. Methods Appl. Sci. 34 (2011), 1667-1684.
• Efendiev, M. A., Sonner, S., On verifying mathematical models with diffusion, transport and interaction, GATUKO Internat. Ser. Math. Sci. Appl. 32 (2010), 41-67.
• Efendiev, M. A., Lasser, R., Sonner, S., Necessary and sufficient conditions for an infinite system of parabolic equations preserving the positive cone, Internat. J. Biomath. Biostat. 1 (2010), 47-52.

Theses

• PhD, Systems of Quasi-Linear PDEs Arising in the Modelling of Biofilms and Related Dynamical Questions, Technische Universität München, 2012.
• Diploma, Twisted Subgroups and Their Conjugacy Classes in Equivariant Degree Theory: Computational Tools and Their Theoretical Background, Ludwig-Maximilians-Universität München, 2008.