The Existence, Local Uniqueness, and Asymptotic Stability of the Boundary Layer Type Solution of the Neumann Problem for a Two-Equation Nonlinear System with Different Powers of a Small Parameter
Б. В. Тищенко
Abstract
In this paper, we consider the existence, local uniqueness, and asymptotic stability of a solution of the boundary-layer type for a nonlinear one-dimensional initial-boundary problem with inhomogeneous Neumann conditions. The corresponding theorems are proved for different types of quasimonotone right-hand sides of the equations by the method of upper and lower solutions and its modification; namely, the asymptotical method of differential inequalities.
Topics & Concepts
UniquenessMathematicsNeumann boundary conditionMathematical analysisType (biology)Nonlinear systemExponential stabilityBoundary value problemStability (learning theory)Boundary (topology)PhysicsComputer scienceEcologyMachine learningQuantum mechanicsBiologyDifferential Equations and Numerical MethodsDifferential Equations and Boundary ProblemsAdvanced Mathematical Modeling in Engineering