A real-valued function <f>(x, y) is called biharmonic in a domain D when the
Chapter 20, Problem 27(choose chapter or problem)
A real-valued function (x, y) is called biharmonic in a domain D when the fourth-order differential equation a4 a4 a4 - +2-- +- =0 ax4 ax2ay2 ay4 at all points in D. Examples of biharmonic functions are the Airy stress function in the mechanics of solids and velocity potentials in the analysis of viscous fluid flow. (a) Show that if> is biharmonic in D, then u = a2!ax2 + a2Jay2 is harmonic in D. (b) If g(z) is analytic inD and (x, y) = Re(z g(z)), show that >is biharmonic in D.
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