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Volume 4,     Number 3,     Summer 1996

 

NONLINEAR EIGENFUNCTION EXPANSION FOR A
PROBLEM IN MICROWAVE HEATING
K.K. TAM, ANDONOWATI AND M.T. KIANG

Abstract. We consider a semi-linear elliptic equation in a bounded domain D with homogeneous boundary conditions arising from microwave heating and develop an eigenfunction expansion procedure for the solution. We treat the nonlinear term as providing constraints for the amplitudes of the eigenfunctions and then use an iterative procedure to refine the coefficients of the expansion. When there are multiple solutions, we compute the bifurcation diagrams.

 

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