André Henrik Erhardt
My research focuses on Partial Differential Equations, Calculus of Variations, Dynamical Systems and Applications in the Life Sciences.
In the field of nonlinear PDEs I am working on existence and regularity theory for parabolic PDEs and obstacle problems. Here, I am interested amongst others in nonstandard growth problems motivated, e.g., by electro-rheological fluids.
Moreover, my second research area is focused on dynamical systems, bifurcation theory, multiple time scale dynamics, geometric singular perturbation theory and the study of complex dyncamics. One application is the mathematical and numerical investigation of cardiac arrhythmia, e.g., the so-called early afterdepolarizations.
In general, I am interested in several applications and problems, e.g., from fluid mechanics or biology modelled by differential equations, i.e., ODEs as well as PDEs. My research is focused on Pure and Applied Mathematics.
- Nonlinear PDEs and dynamics
- Existence and regularity theory
- Bifurcation and stability theory
- (Geometric) singular perturbation theory
- Mathematical and computational neuroscience
Further information about my research, mainly my full publication list in cristin (see below) or on ORCID and most of my citations, can be found here:
- MathSciNet (edited by American Mathematical Society, login required)
- Scopus (edited by Elsevier)
- zbMATH (edited by the European Mathematical Society (EMS), the Heidelberg Academy of Sciences and Humanities and FIZ Karlsruhe)
Conferences and workshops:
10/2018: Workshop on "Analysis and PDE", Hannover, Germany
06/2018: Lund Workshop on "Fluid Dynamics and Dispersive Equations", Lund, Sweden
04/2018: INdAM Workshop: "Mathematical and Numerical Modeling of the Cardiovascular System", Roma, Italy
03/2018: The 60th British Applied Mathematics Colloquium (BAMC 2018), St Andrews, Scotland, UK
- Erhardt, André H (2018). Bifurcation Analysis of a Certain Hodgkin-Huxley Model Depending on Multiple Bifurcation Parameters. Mathematics. ISSN 2227-7390. 6(6), s 1- 15 . doi: 10.3390/math6060103
- Erhardt, André H (2017). The stability of parabolic problems with nonstandard p(x,t)-growth. Mathematics. ISSN 2227-7390. 5(4), s 1- 14 . doi: 10.3390/math5040050 Full text in Research Archive.
- Erhardt, André H (2017). Compact embedding for p(x,t)-Sobolev spaces and existence theory to parabolic equations with p(x,t)-growth. Revista Matemática Complutense. ISSN 1139-1138. 30(1), s 35- 61 . doi: 10.1007/s13163-016-0211-4
- Kügler, P.; Bulelzai, Mak & Erhardt, André H (2017). Period Doubling Cascades of Limit Cycles in Cardiac Action Potential Models as Precursors to Chaotic Early Afterdepolarizations. BMC Systems Biology. ISSN 1752-0509. 11, s 1- 13 . doi: 10.1186/s12918-017-0422-4
- Erhardt, André H (2016). Existence of solutions to parabolic problems with nonstandard growth and irregular obstacles. Advances in Differential Equations. ISSN 1079-9389. 21(5-6), s 463- 504
- Erhardt, André H (2016). Higher integrability for solutions to parabolic problems with irregular obstacles and nonstandard growth. Journal of Mathematical Analysis and Applications. ISSN 0022-247X. 435(2), s 1772- 1803 . doi: 10.1016/j.jmaa.2015.11.028
- Erhardt, André H (2016). Regularity results for nonlinear parabolic obstacle problems with subquadratic growth. Journal of Differential Equations. ISSN 0022-0396. 261(12), s 6915- 6949 . doi: 10.1016/j.jde.2016.09.006
- Erhardt, André H (2015). Hölder estimates for parabolic obstacle problems. Annali di Matematica Pura ed Applicata. ISSN 0373-3114. 194(3), s 645- 671 . doi: 10.1007/s10231-013-0392-0
- Erhardt, André H (2015). On the Calderón-Zygmund theory for parabolic problems with nonstandard growth condition. Journal of Mathematics Research. ISSN 1916-9795. 7(1), s 10- 36 . doi: 10.5539/jmr.v1n1p10
- Erhardt, André (2014). Calderón-Zygmund theory for parabolic obstacle problems with nonstandard growth. Advances in Nonlinear Analysis. ISSN 2191-9496. 3(1), s 15- 44 . doi: 10.1515/anona-2013-0024