Book ChapterDOI
Comparison Principle for Reaction-Diffusion-Advection Problems with Boundary and Internal Layers
N. N. Nefedov
- pp 62-72
TLDR
The theorems which state front motion description and stationary contrast structures formation are proved for parabolic, parabolic-periodic and integro-parabolic problems are proved.Abstract:
In the present paper we discuss father development of the general scheme of the asymptotic method of differential inequalities and illustrate it applying for some new important cases of initial boundary value problem for the nonlinear singularly perturbed parabolic equations,which are called in applications as reaction-diffusion-advection equations. The theorems which state front motion description and stationary contrast structures formation are proved for parabolic, parabolic-periodic and integro-parabolic problems.read more
Citations
More filters
Journal ArticleDOI
Internal layers in the one-dimensional reaction–diffusion equation with a discontinuous reactive term
N. N. Nefedov,Minkang Ni +1 more
TL;DR: In this paper, a singularly perturbed boundary value problem for a second-order ordinary differential equation known in applications as a stationary reaction-diffusion equation was studied, and the existence of solutions with an internal transition layer was proved.
Journal ArticleDOI
On Front Motion in a Burgers-Type Equation with Quadratic and Modular Nonlinearity and Nonlinear Amplification
N. N. Nefedov,Oleg Rudenko +1 more
TL;DR: In this article, a singularly perturbed initial-boundary value problem for a parabolic equation known as a Burgers-type or reaction-diffusion-advection equation is considered.
Journal ArticleDOI
The solution with internal transition layer of the reaction-diffusion equation in case of discontinuous reactive and diffusive terms
Journal ArticleDOI
Time-periodic boundary layer solutions to singularly perturbed parabolic problems
TL;DR: In this paper, the authors present a result of implicit function theorem type for singularly perturbed problems based on fixed point iterations for contractive mappings, in particular, no monotonicity or sign preservation properties are needed.
Journal ArticleDOI
Existence and Stability of Solutions with Boundary Layers in Multidimensional Singularly Perturbed Reaction-Diffusion-Advection Problems
TL;DR: In this article, the boundary value problem for a nonlinear elliptic equation containing a small parameter multiplying the derivatives and degenerating into a finite equation as the small parameter tends to zero is dealt with.
References
More filters
Book ChapterDOI
Periodic Solutions of Semilinear Parabolic Equations
TL;DR: In this article, the authors describe the methods of nonlinear functional analysis, namely, fixed-point theorems in ordered Banach spaces, to prove existence and multiplicity result for periodic solutions of semilinear parabolic differential equations of the second order.
Journal ArticleDOI
Singularly perturbed problems with boundary and internal layers
TL;DR: In this paper, the authors present a brief survey and describe new ideas and methods of analysis in the asymptotic theory of solutions with internal layers, which is one of the topical fields of singular perturbation theory.