I undertake research into nonlinear partial differential equations, employing a combination of analytical and numerical techniques in their study. I am particularly interested in studying free boundary problems arising from thin film flows, including investigations of rupture phenomena, moving contact lines and the effects of surface topography and driving forces upon the motion of the liquid. Such problems often yield evolution equations for the interfacial film thickness in the form of high-order degenerate parabolic equations.

I am currently Chair of the Major in Mathematical Sciences here at Waseda University.

## Research Articles

- Cauchy-Dirichlet Problems for the Porous Medium Equation, M. Bowen, J. R. King and T. P. Witelski,
*Disc. Cont. Dyn. Sys.*, 2023, 43(3&4): 1143-1174. doi: 10.3934/dcds.2022182 - Pressure-dipole solutions of the thin-film equation, M. Bowen and T. P. Witelski,
*Euro. J. Appl. Math.*, 30 (2), 358-399, 2019. - On self-similar thermal rupture of thin liquid sheets, M. Bowen and B. S. Tilley
*Phys. Flu.,*25 (10), 102105, 2013. - Dynamics of a viscous thread on a non-planar substrate, M. Bowen and J. R. King,
*J. Eng. Math.,*80 (1), 39-62, 2013. - Thermally induced van der Waals rupture of thin viscous fluid sheets, M. Bowen and B. S. Tilley,
*Phys. Flu.,*24 (3), 032106, 2012. - The linear limit of the dipole problem for the thin film equation, M. Bowen and T. P. Witelski,
*SIAM J. Appl. Math.,*66 (5), 1727-1748, 2006. - Thermocapillary control of rupture in thin viscous fluid sheets, B. S. Tilley and M. Bowen,
*J. Flu. Mech.*, 541, 399, 2005. - Nonlinear dynamics of two-dimensional undercompressive shocks, M. Bowen, J. Sur, A. L. Bertozzi, R. P. Behringer, Physica D, 209 (1-4), 36-48, 2005.
- The self-similar solution for draining in the thin film equation, J. B. Van Den Berg, M. Bowen, J. R. King, M. M. A. El-Sheikh,
*Euro. J. Appl. Math.,*15 (3), 329, 2004. - ADI schemes for higher-order nonlinear diffusion equations, T. P. Witelski and M. Bowen,
*Appl. Num. Math.,*45 (2-3), 331-351, 2003 - Thin film dynamics: theory and applications, A. L. Bertozzi and M. Bowen,
*Modern Methods in Scientific Computing and Applications*, 31-79, 2002. - Intermediate asymptotics of the porous medium equation with sign changes, J. Hulshof, J. R. King, M. Bowen,
*Adv Diff. Eq.,*6 (9), 1115-1152, 2001. - Anomalous exponents and dipole solutions for the thin film equation, J. Hulshof, J. R. King, M. Bowen.,
*SIAM J. Appl. Math.,*62 (1), 149-179, 2001. - Moving boundary problems and non-uniqueness for the thin film equation, J. R. King and M. Bowen,
*Euro. J. Appl. Math*., 12, 321356, 2001. - Asymptotic behaviour of the thin film equation in bounded domains, M. Bowen and J. R. King,
*Euro. J. Appl. Math.*, 12 (2), 135-157, 2001.

#### Interdisciplinary articles

- The Language of Mathematics: A Corpus-based Analysis of Research Article Writing in a Neglected Field, L. Anthony and M. Bowen,
*Asian ESP J.*, 9(2), 5-25, 2013.

#### Online material

- Singular perturbation theory, T. P. Witelski and M. Bowen, Scholarpedia 4 (4), 3951, 2009.

#### Books

Errata for the textbook can be found here. Please email me with any errata/typos that you find.

## Teaching

I currently teach classes in multivariable calculus and analysis. I also teach a “reading course” in which students read parts of a popular science book (currently *Chaos: Making a New Science* by James Gleick) and then in class we explore the mathematics discussed in the book.

I have previously taught classes in single variable calculus, linear algebra, ordinary differential equations, partial differential equations, nonlinear dynamics, computational methods, asymptotics and perturbation methods, and fluid mechanics.

#### President’s Award

I was awarded the President’s Award for Teaching (Spring Semester 2015) by President Kamata of Waseda University.

#### An example lecture

In the calculus courses, we start from first principles, proving all of the important results as we progress towards increasingly more advanced concepts.

In 2019, I gave a “non-technical” introductory lecture to prospective students (and families) visiting Waseda University for an open day, as an example of the kind of material that would be presented at the very beginning of an introductory calculus course. This lecture can be found on YouTube as *Mathematics in Action*.

## Society Membership

- American Physical Society (APS)
- Society for Industrial and Applied Mathematics (SIAM)
- I am one of the faculty advisors for the Waseda SIAM Student Chapter

- Japanese Society for Industrial and Applied Mathematics (JSIAM)
- Mathematical Society of Japan
- Japan Society of Fluid Mechanics