Traveling waves for bistable reaction–diffusion–convection equations with discontinuous density-dependent coefficients

Abstract Continuing our previous study (P. Drábek, S. Jung, E. Ko, and M. Zahradníková, Traveling waves for monostable reaction-diffusion-convection equations with discontinuous density-dependent coefficients , J. Math. Anal. Appl. 539 (2024), no. 1, part 1, 26) on the monostable reaction–diffusion–convection equation, we analyze the bistable case under weak regularity assumptions. Our approach applies monostable results on the subintervals where the reaction term g has constant sign, thereby establishing both existence and nonexistence of bistable traveling wave solutions. We extend the results of (L. Malaguti, C. Marcelli, and S. Matucci, Front propagation in bistable reaction-diffusion-advection equations , Adv. Differential Equations 9 (2004), no. 9–10, 1143–1166), obtained for p = 2 under higher regularity assumptions ( d ∈ C 1 [0, 1], g , h ∈ C [0, 1]), to the p -Laplacian with p > 1 in our weak regularity setting.