The simplest problem with boundary layers, $\epsilon ^{2}u_{xx}-u=-f(x)$, is used to illustrate (i) why the perturbation series in powers of ε is asymptotic but divergent, (ii) why the optimally ...

R. E. O'Malley, Jr. A basic problem in singular perturabations is to study systems of differential equations whose order is reduced when a small parameter becomes zero. It is important for numerous ...

The National Academies of Sciences, Engineering, and Medicine are private, nonprofit institutions that provide expert advice on some of the most pressing challenges facing the nation and world. Our ...

The mathematical modelling of free and moving boundary problems are an important topic in engineering, industry, technology and theoretical sciences. These models allow us to make calculations ...