Perturbation Methods in Applied Mathematics |
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Introduction | 1 |
Twovariable expansion procedures | 79 |
Applications to partial differential equations | 120 |
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A₁ a² Fo a²u amplitude approximate equations asymptotic expansion at² B₁ behavior boundary condition Equation boundary conditions boundary layer boundary-layer equations C₁ characteristic coefficients consider const constant constructed coordinates corresponding curl differential equations dimensionless distinguished limit dominant dr² dx² equation Equation exact solution example expansion Equation expansion procedure expansion valid exponential exponential decay F₁ Figure fixed flow functions h₁ initial conditions inner expansion intermediate limit inviscid limit process linear Navier-Stokes equations nonlinear ordinary differential equations oscillations outer expansion outer solution partial differential equations periodic solution perturbation phase plane piston potential flow result Section shock waves side of Equation singular solution of Equation subcharacteristic surface theory transonic two-variable u₁ uniformly valid upstream infinity variables velocity viscous zero ду дх