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Existence and Computation of Solutions to the Plasma Physics Hasegawa-Mima Equation
A seminar to be conducted by Nabil Nassif, Department of Mathematics, American University of Beirut (AUB)
We represent the highly non-linear Hasegawa-Mima PDE model as a coupled system of Elliptic-Hyperbolic PDEs, each being linear. We apply the Petrov-Galerkin method to obtain a sequence of fixed-point approximate solutions that converge weakly to a solution that satisfies periodic boundary conditions. We obtain existence results under weak assumptions on the initial data. Furthermore, the new-coupled mathematical model appears well suitable for Finite Element discretization. Preliminary numerical results for the simulation model are presented.
Speaker: Professor Nabil Nassif is a professor of Mathematics at the American University of Beirut (AUB). His area of research is in ODE and numerical methods.