Elsevier Acta Medica Okayama 02941449 36 7 2019 Axially asymmetric traveling fronts in balanced bistable reaction-diffusion equations 1791 1816 EN Masaharu Taniguchi Research Institute for Interdisciplinary Science, Okayama University For a balanced bistable reaction-diffusion equation, an axisymmetric traveling front has been well known. This paper proves that an axially asymmetric traveling front with any positive speed does exist in a balanced bistable reaction-diffusion equation. Our method is as follows. We use a pyramidal traveling front for an unbalanced reaction-diffusion equation whose cross section has a major axis and a minor axis. Preserving the ratio of the major axis and a minor axis to be a constant and taking the balanced limit, we obtain a traveling front in a balanced bistable reaction-diffusion equation. This traveling front is monotone decreasing with respect to the traveling axis, and its cross section is a compact set with a major axis and a minor axis when the constant ratio is not 1. No potential conflict of interest relevant to this article was reported.