Biography

Dr. John Meyer, Associate Professor in Applied Mathematics.

Contact details

Email：j.c.meyer@bham.ac.uk

Qualifications

Member of the Institute of Mathematics and its Applications (2019)

Postgraduate certificate in Academic Practice (2018)

Member of the London Mathematical Society (2016)

Fellow of the Higher Education Academy (2016)

PhD in Applied Mathematics, University of Birmingham (2013)

MSci (Hons) in Mathematical Sciences, University of Birmingham (2009)

Research

Research Themes

Qualitative theory for solutions to boundary value problems for elliptic/parabolic PDE

Maximum & Tangency principles for elliptic/parabolic PDE

E-assessment of mathematics

Research Activity

Reaction-Diffusion Theory – Specifically in the local but non-Lipschitz nonlinearity setting, and the regular non-local nonlinearity setting. Primarily concerning well-posedness, but also counter-intuitive qualitative properties of solutions.

Maximum & Tangency Principles - These provide qualitative information about solutions to boundary value problems for elliptic and parabolic partial differential inequalities.

Applied analysis on mathematical models arising from heat and mass transfer, chemical reaction kinetics, and mathematical physics.

Mathematics Education – Specifically related to e-assessment.

Publications

Book

Meyer, J & Needham, D 2015, The cauchy problem for non-lipschitz semi-linear parabolic partial differential equations. London Mathematical Society Lecture Note Series, no. 419, Cambridge University Press, Cambridge, UK. https://doi.org/10.1017/CBO9781316151037

Article

Needham, D, Meyer, J, Billingham, J & Drysdale, C 2023, 'The Riemann problem for a generalized Burgers equation with spatially decaying sound speed: I Large-time asymptotics', Studies in Applied Mathematics, vol. 150, no. 4, pp. 963-995. https://doi.org/10.1111/sapm.12561

Kinnear, G, Jones, I, Sangwin, C, Alarfaj, M, Davies, B, Fearn, S, Foster, C, Heck, A, Henderson, K, Hunt, T, Iannone, P, Kontorovich, I, Larson, N, Lowe, T, Meyer, J, O’Shea, A, Rowlett, P, Sikurajapathi, I & Wong, T 2022, 'A collaboratively-derived research agenda for e-assessment in undergraduate mathematics', International Journal of Research in Undergraduate Mathematics Education. https://doi.org/10.1007/s40753-022-00189-6

Meyer, J 2022, 'A note on boundary point principles for partial differential inequalities of elliptic type', Boundary Value Problems, vol. 2022, no. 1, 33, pp. 1-20. https://doi.org/10.1186/s13661-022-01614-0

Meyer, J 2021, 'A note on radio wave propagation' Mathematics Today, vol. 57, no. 2, pp. 61-63.

Jones, D, Meyer, J & Huang, J 2021, 'Reflections on remote teaching', MSOR Connections, vol. 19, no. 1, pp. 47-54. https://doi.org/10.21100/msor.v19i1.1137

Mason, S, Meyer, J & Needham, D 2021, 'The development of a wax layer on the interior wall of a circular pipe transporting heated oil: the effects of temperature-dependent wax conductivity', Journal of Engineering Mathematics, vol. 131, 7. https://doi.org/10.1007/s10665-021-10171-x

Clark, V & Meyer, J 2020, 'On two-signed solutions to a second order semi-linear parabolic partial differential equation with non-Lipschitz nonlinearity', Journal of Differential Equations, vol. 269, no. 2, pp. 1401-1431. https://doi.org/10.1016/j.jde.2020.01.007

Meyer, J & Needham, D 2018, 'On a L∞ functional derivative estimate relating to the Cauchy problem for scalar semi-linear parabolic partial differential equations with general continuous nonlinearity', Journal of Differential Equations, vol. 265, no. 8, pp. 3345-3362. https://doi.org/10.1016/j.jde.2018.04.051

Meyer, J & Needham, D 2017, 'The evolution to localized and front solutions in a non-Lipschitz reaction-diffusion Cauchy problem with trivial initial data', Journal of Differential Equations, vol. 262, no. 3, pp. 1747-1776. https://doi.org/10.1016/j.jde.2016.10.027

Meyer, JC & Needham, DJ 2016, 'Aspects of Hadamard well-posedness for classes of non-Lipschitz semilinear parabolic partial differential equations', Proceedings of the Royal Society of Edinburgh: Section A (Mathematics), vol. 146, no. 4, pp. 777-832. https://doi.org/10.1017/S0308210515000712

Needham, DJ & Meyer, JC 2015, 'A note on the classical weak and strong maximum principles for linear parabolic partial differential inequalities', Zeitschrift für angewandte Mathematik und Physik, vol. 66, no. 4, pp. 2081-2086. https://doi.org/10.1007/s00033-014-0492-8

Meyer, JC & Needham, DJ 2015, 'Well-posedness and qualitative behaviour of a semi-linear parabolic Cauchy problem arising from a generic model for fractional-order autocatalysis', Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences, vol. 471, no. 2175, 20140632. https://doi.org/10.1098/rspa.2014.0632

Meyer, JC & Needham, DJ 2014, 'Extended weak maximum principles for parabolic partial differential inequalities on unbounded domains', Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences, vol. 470, no. 2167, 20140079. https://doi.org/10.1098/rspa.2014.0079