Mathematical Sciences: Asymptotic Analysis of Singular Bifurcation, Limit Point Instabilities and Free Boundary Problems and Applications

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This research program considers a series of mathematical problems connected with singular bifurcation equations, limit point instabilities and free boundary problems. They include effects of time- dependent parameters, steady bifurcation and Hopf bifurcation with a slowly varying control, slow passage through a critical point, transition to periodic solutions from a homoclinic orbit, etc. The research results will have direct applications to laser problems and polymer devices, especially in the rate of drug release from capsules.