8692

8073

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1392

هشت،68ص.

ص.ع.به فارسي و انگليسي

محمدرضا رئوفي

مجيد گازر

20/1/93

مهدي تاتاري، رضا مزروعي سبداني

رياضي

ID8073

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Eigenvalues Of The Stokes Operator Versus The Dirichlet Laplacian In The Plane Ziba Tayebinezhad z tayebinezhad@math iut ac ir 2013 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mohammad Reza Raoo raoo @cc iut ac ir Advisor Dr Majid Gazor mgazor@cc iut ac ir 2010 MSC 35P99 Keywords Dirichlet Laplacian Stokes operator Navier slip boundary conditions AbstractIn this thesis we invastigate the inequality betwen eigenvalues of Dirichlet Laplacian and Stokes op erators on the one hand and between Dirichlet Laplacian and Neumann Laplacian on the other hand We show that the k th eigenvalue of the Dirichlet Laplacian is strictly less than the k th eigenvalueof the classical Stokes operator equivalently of the clamped buckling plate problem for a boundeddomain in the plane having a locally Lipschitz boundary For a C 2 boundary we show that eigen values of the Stokes operator with Navier slip boundary conditions interpolate continuously betweeneigenvalues of the Dirichlet Laplacian and of the classical Stokes operator We use Filonov s original idea used rst in proving the inequality between Dirichlet and Neumann Laplacian operators to proves both inequalities This paper is organized as follows We describe the necessary function spaces trace operators andrelated lemmas in Section 2 In Section 4 we de ne the classical Stokes operator and a variant of itusing Lions boundary conditions vanishing vorticity on the boundary We show that the eigenvalueproblem for the classical Stokes operator is equivalent to the eigenvalue problem for the clamped buck ling plate problem We also describe the strong forms of the associated eigenvalue problems in Section4 giving the weak forms in Section 5 In Section 6 we describe the variational min max formulationsof the eigenvalue problems using these formulations in Section 7 to prove important Theorem In

محمدرضا رئوفي

مجيد گازر

مهدي تاتاري، رضا مزروعي سبداني