Propagation of calcium waves in a bistable buffered system with nonlocal dispersal

We investigate wave propagation in a bistable buffered system with nonlocal dispersal. A central question in this problem is the effect of stationary buffers on calcium waves. In this paper, we first establish the existence of bistable traveling waves, demonstrating that the buffers cannot eliminate the presence of calcium waves. We then investigate the range and sign of their speeds. We observe a new phenomenon: while the buffers do not alter the propagation direction of the calcium waves, they can reduce the speed of these waves. Finally, we establish the exact asymptotic behavior of the traveling waves at infinity and prove a form of stability for a pair of diverging traveling waves. Consequently, we derive a sufficient condition for solutions to converge to the larger stable equilibria.