On Extension of Asymptotic Comparison Principle for Time Periodic Reaction-Diffusion-Advection Systems with Boundary and Internal Layers
In this paper we present a further development of our asymptotic comparison principle, applying it for some new important classes of initial boundary value problem for the nonlinear singularly perturbed time periodic parabolic equations, which are called in applications as reaction-diffusion-advection equations. We illustrate our approach for the new problem with balanced nonlinearity. The theorems, which states the existence of the periodic solution with internal layer, gives it’s asymptotic approximation and state their Lyapunov stability are proved.
KeywordsSingularly perturbed problems Moving fronts Time periodic reaction-diffusion-advection equations
This work is supported by RFBR, pr. N 13-01-91333.
- 1.Vasilieva, A.B., Butuzov, V.F., Nefedov, N.N.: Contrast structures in singularly perturbed problems. Fundamentalnaja i prikladnala matematika 4(3), 799–851 (1998)Google Scholar
- 4.Hess, P.: Periodic-Parabolic Boundary Value Problems and Positivity, Pitman Research Notes in Math. Series 247. Longman Scientific and Technical, Harlow (1991)Google Scholar
- 5.Zabrejko, P.P., Koshelev, A.I., et al.: Integral Equations. M.Nauka, Moscow (1968) Google Scholar