In this project, we study the periodic Dirichlet boundary value problem for a singularly perturbed reaction-advection-diffusion equation on the segment in case of discontinuous reactive and convective terms. Applying the boundary function method, we construct the asymptotic approximation of the periodic solution with internal transition layer located in the vicinity of a curve of discontinuity of the mentioned terms. For the problem here we prove the existence of the periodic solution, estimate the accuracy of the asymptotical approximation and investigate the stability of the periodic solution as solutions of the corresponding initial boundary value problems for the reaction-advection-diffusion equation.

在这个项目中，我们研究了在反应性和对流项不连续的情况下，该段上的奇摄动反应-对流-扩散方程的周期Dirichlet边值问题。应用边界函数法，我们构造了周期解的渐近逼近，其中内部过渡层位于所提及项的不连续曲线的附近。对于这里的问题，我们证明了周期解的存在性，估计了渐近逼近的精度，并研究了周期解的稳定性，以作为反应对流扩散方程相应初始边值问题的解。