Interests
- Nonlinear (multi-scale) partial differential systems (arising in fluid dynamics and evolving microstructures): Weak solvability, regularity, boundedness, etc.
- Degenerating parabolic equations: Existence of weak solutions by regularization
- Mathematical modeling of biological processes (biofilms, chemotaxis, etc.) in evolving microstructures: Homogenization in a level-set framework
- Numerical analysis of nonlinear (multi-scale) PDE systems: (Upwind, mixed) finite element methods
Publications
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Existence and uniqueness of solutions to a flow and transport problem with degenerating coefficients
In: European Journal of Applied Mathematics (2022)
ISSN: 0956-7925
DOI: 10.1017/S0956792522000018
BibTeX: Download - , , , , , , , , , , , , , , , , , , , , , , , , :
Linking rhizosphere processes across scales: Opinion
In: Plant and Soil (2022)
ISSN: 0032-079X
DOI: 10.1007/s11104-022-05306-7
URL: https://link.springer.com/article/10.1007/s11104-022-05306-7
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Degenerate equations for flow and transport in clogging porous media
In: Journal of Mathematical Analysis and Applications 483 (2020), Article No.: 123613
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2019.123613
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Degenerate equations in a diffusion-precipitation model for clogging porous media
In: European Journal of Applied Mathematics (2020)
ISSN: 0956-7925
DOI: 10.1017/S0956792519000391
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Mit Mathe richtig anfangen Eine Einführung mit integrierter Anwendung der Programmiersprache Python
Berlin Heidelberg: Springer Spektrum, 2019
ISBN: 978-3-662-59229-8
DOI: 10.1007/978-3-662-59230-4
BibTeX: Download - , :
Derivation of an effective dispersion model for electro-osmotic flow involving free boundaries in a thin strip
In: Journal of Engineering Mathematics (2019)
ISSN: 0022-0833
DOI: 10.1007/s10665-019-10024-8
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Biofilm modeling in evolving porous media with Beavers-Joseph condition
In: ZAMM - Zeitschrift für angewandte Mathematik und Mechanik 99 (2019)
ISSN: 0044-2267
DOI: 10.1002/zamm.201800123
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Crystal precipitation and dissolution in a porous medium: Evolving microstructure and perforated solid matrix
In: Special Topics and Reviews in Porous Media 10 (2019), p. 305-321
ISSN: 2151-4798
DOI: 10.1615/SpecialTopicsRevPorousMedia.2019029274
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Mathematical Modeling and Analysis of Processes in Evolving Microstructures (Habilitation, 2019)
DOI: DOI: 10.1615/SpecialTopicsRevPorousMedia.2019029274
BibTeX: Download - , , , , :
Beyond Kozeny-Carman: Predicting the Permeability in Porous Media
In: Transport in Porous Media (2019)
ISSN: 0169-3913
DOI: 10.1007/s11242-019-01321-y
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Spatial asymptotic profiles of solutions to the Navier-Stokes system in a rotating frame with fast decaying data
In: Journal of the Hokkaido University, Faculty of Science, Series VII: Geophysics 47 (2018), p. 501 - 529
ISSN: 0441-067X
DOI: 10.14492/hokmj/1537948828
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Old and New Approaches Predicting the Diffusion in Porous Media
In: Transport in Porous Media 124 (2018), p. 803-824
ISSN: 0169-3913
DOI: 10.1007/s11242-018-1099-x
URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2018/2018_RayRuppSchulzKn_OldAndNewApproachesPredictingTheDiffInPM
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Analysis of chemotactical biofilm growth in evolving microstructures
88th GAMM Annual Meeting (Weimar, 06.03.2017 - 10.03.2017)
In: Proceedings in Applied Mathematics and Mechanics PAMM 2017
DOI: 10.1002/pamm.201710326
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Boundedness in a biofilm-chemotaxis model in evolving porous media
In: Mathematical Modelling and Analysis 22 (2017), p. 852-869
ISSN: 1392-6292
DOI: 10.3846/13926292.2017.1389772
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An effective model for biofilm growth made by chemotactical bacteria in evolving porous media
In: SIAM Journal on Applied Mathematics 77 (2017), p. 1653-1677
ISSN: 0036-1399
DOI: 10.1137/16M108817X
URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2017/2017_SchulzKn_AnEffectiveModelForBiofilmGrowthInEvolvinPM
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Derivation and analysis of an effective model for biofilm growth in evolving porous media
In: Mathematical Methods in the Applied Sciences 40 (2017), p. 2930-2948
ISSN: 0170-4214
DOI: 10.1002/mma.4211
URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2017/2017_SchulzKn_DerivAnalysOfEffectModelForBiofilmGrowthInEvolvPM
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Strong solvability up to clogging of an effective diffusion-precipitation model in an evolving porous medium
In: European Journal of Applied Mathematics (2016), p. 1-29
ISSN: 0956-7925
DOI: 10.1017/S0956792516000164
URL: https://www1.am.uni-erlangen.de/research/publications/Jahr_2016/2016_SchulzRayFrankMahatoKn_StrongSolvUpToCloggingInAnEvolvingPM
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Concentration-diffusion phenomena of heat convection in an incompressible fluid
In: Asymptotic Analysis 88 (2014), p. 17 - 41
ISSN: 0921-7134
DOI: 10.3233/ASY-131211
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Spatial Asymptotic Profile in Geophysical Fluid Dynamics (Dissertation, 2012)
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Projects
Multiscale modeling with evolving microstructure: An approach to emergence in the rhizosphere via effective soil functions
Term: 01.02.2019 - 31.01.2022
Funding source: DFG / Schwerpunktprogramm (SPP)
Project leader: ,
Funding source: DFG / Schwerpunktprogramm (SPP)
Project leader: ,
The self-organization of the aggregates in the rhizosphere by variousattracting forces influenced by geochemistry, and microbiology shallbe studied by a novel, comprehensive model. This model shouldaccount for processes on the microscale (single roots, pore scale),and then be upscaled to the root system scale (macroscale) bymathematical homogenization. This goal exceeds the functional rangeof existing models for aggregation and needs the introduction of anexplicit phase of mucilage, and attachme…
DAAD PPP: German-Norwegian collaborative research support scheme
Term: 01.01.2016 - 31.12.2017
Funding source: Deutscher Akademischer Austauschdienst (DAAD)
Acronym: DAAD PPP
Project leader: ,
Funding source: Deutscher Akademischer Austauschdienst (DAAD)
Acronym: DAAD PPP
Project leader: ,
Homogenisierung reaktiven Transports in variablen Mikrostrukturen