On the Asymptotic Solution of a Two-Parameter Boundary Value Problem of Chemical Reactor Theory

Source abstract

The paper provides an asymptotic solution to boundary value problems of the form \[ \begin{gathered} \varepsilon _1 y'' + a(x)y' = f(x,y,z),\quad \varepsilon _1 \varepsilon _2 z'' + b(x)z' = g(x,y,z), \hfill \\ y'(0) = z'(0) = 0,\quad \varepsilon _1 y'(1) + y(1) = A,\quad \varepsilon _1 \varepsilon _2 z'(1) + z(1) = B, \hfill \\ \end{gathered} \] where $\varepsilon _1$ and $\varepsilon _2$ are small positive parameters simultaneously tending to zero, a and b are strictly positive, and $a,b,f$, and g are infinitely differentiable in their arguments.