Nonlinear Stability Analysis of Stationary Solutions for A Special Class of Reaction-diffusion-convection Systems With Respect To Small Perturbation

We study the stability of multidimensional planar fronts for a reaction-diffusionconvection system introduced in combustion theory with respect to spatially localized perturbations. In the thesis, we investigate the nonlinear stability of the trivial solution with respect to a small perturbation. For the reaction-diffusion-convection system in multidimensional space, we employ exponentially weighted spaces to shift the spectrum of the linearized differential operator and determine the spectrum of the equations after adding the drift term. We analyze the nonlinear equations on the intersection of the unweighted and weighted space. We demonstrate that the unweighted norm of the equations is bounded by small initials and and that the weighted norm decays algebraically as time progresses.