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, since 2014 I am extending my fields of interest to my second research area: dynamical systems, bifurcation theory, multiple time scale dynamics and geometric singular perturbation theory. One main 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 Theory
- Regularity Theory
- Stability Theory
- Bifurcation Theory
- (Geometric) Singular Perturbation Theory
Further information about my research, mainly my publication list and (most) citations, can be found here:
- 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