Front Motion in a Problem with Weak Advection in the Case of a Continuous Source and a Modular-Type Source
Н. Н. Нефедов, E. I. Nikulin, А. О. Орлов
Abstract
We obtain an asymptotic approximation to a moving inner layer (front) solution of an initial–boundary value problem for a singularly perturbed parabolic reaction–advection–diffusion equation with small advection. We separately consider the case of a continuous source (the nonlinearity describing the interaction and reaction) and the case of a source discontinuity for a certain value of the unknown function, which arises in a number of topical applications. For either problem, an asymptotic approximation to the solution is constructed and existence and uniqueness theorems for such a solution are proved.
Topics & Concepts
MathematicsDiscontinuity (linguistics)AdvectionUniquenessOrdinary differential equationMathematical analysisPartial differential equationBoundary value problemInitial value problemDifferential equationPhysicsThermodynamicsDifferential Equations and Numerical MethodsAdvanced Mathematical Modeling in EngineeringDifferential Equations and Boundary Problems