Consider again Robin BCs at both ends for arbitrary a0 and

Chapter 4, Problem 4.3.8

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Consider again Robin BCs at both ends for arbitrary a0 and al. (a) In the a0al plane sketch the hyperbola a0 +al = a0all. Indicate theasymptotes.For(a0,al)onthishyperbola,zeroisaneigenvalue, according to Exercise 2(a). (b) Show that the hyperbola separates the whole plane into three regions, depending on whether there are two, one, or no negative eigenvalues. (c) Label the directions of increasing absorption and radiation on each axis. Label the point corresponding to Neumann BCs. (d) Where in the plane do the Dirichlet BCs belong?

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