Evolution of reaction-diffusion patterns in infinite and bounded domains

摘要: Abstract We introduce a semi-analytical method to study the evolution of spatial structures in reaction-diffusion systems. It consists writing an integral equation for relevant densities, from propagator linear part operator. In order test method, we perform exhaustive one-dimensional model associated electrical device - ballast resistor. consider step and bubble-shaped initial density profiles free space as well semi-infinite domain with Dirichlet Neumann boundary conditions. The piecewise-linear form reaction term, which preserves basic ingredients more complex nonlinear models, makes it possible obtain exact wave-front solutions stationary bounded domain. Short long-time behaviour can also be analytically studied, whereas at intermediate times is analyzed by numerical techniques. paid particular attention features introduced