This issue of the Japan Journal of Industrial and Applied Mathematics contains 13 peer-reviewed articles submitted by the participants of the Czech-Japanese Seminar in Applied Mathematics 2021 held on January 5–7, 2021 online by the Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Czech Republic.

Since 2004, the Czech-Japanese Seminar in Applied Mathematics has been continued as a series. The first one took place in Prague in 2004, the second one was held in Kuju, Kyushu in 2005, the third one was organized in Prague in 2006, the fourth in Takachiho, Miyazaki in 2008, the fifth in Prague and Telč in 2010, the sixth in Tokyo in 2013, the seventh in Krakow, Poland in 2016 and the eighth in Noto, Ishikawa in 2018.

The purpose of it as an international conference has always been getting together applied mathematicians dealing with mathematical modelling, mathematical and numerical analyses of nonlinear partial differential equations applied namely in material sciences, biology, computer science and medicine. Central themes are: ordinary differential equations, partial differential equations, dynamical systems, computational fluid dynamics, image processing and computer vision, numerical analysis, computational finance, inverse problems, engineering techniques and modelling of physical phenomena.

Finally, we thank all the authors for their contributions and the reviewers for their efforts.