On the spectral representation for singular selfadjoint boundary eigenvalue problems

1998 ◽  
pp. 217-251 ◽  
Author(s):  
Don Hinton ◽  
Albert Schneider
Keyword(s):  
Spectral Representation ◽  
Eigenvalue Problems ◽  
Boundary Eigenvalue

Fréedericksz transitions in nematic liquid crystals as boundary eigenvalue problems

2007 ◽  
Vol 80 (6-7) ◽  
pp. 675-685
Author(s):  
Jerzy KĘdzierski ◽  
Marek Andrzej Kojdecki ◽  
Zbigniew Raszewski ◽  
Jerzy Zieliński
Keyword(s):  
Liquid Crystals ◽  
Eigenvalue Problems ◽  
Nematic Liquid Crystals ◽  
Boundary Eigenvalue

scholarly journals Eigenvalue enclosures and exclosures for non-self-adjoint problems in hydrodynamics

2010 ◽  
Vol 13 ◽  
pp. 65-81 ◽  
Author(s):  
B. Malcolm Brown ◽  
Matthias Langer ◽  
Marco Marletta ◽  
Christiane Tretter ◽  
Markus Wagenhofer
Keyword(s):  
Eigenvalue Problems ◽  
Wave Number ◽  
Computer Assisted ◽  
Inviscid Fluid ◽  
Natural Oscillations ◽  
Highly Sensitive ◽  
Elliptical Flow ◽  
Boundary Eigenvalue ◽  
Unstable Part ◽  
Sommerfeld Equation

AbstractIn this paper we present computer-assisted proofs of a number of results in theoretical fluid dynamics and in quantum mechanics. An algorithm based on interval arithmetic yields provably correct eigenvalue enclosures and exclosures for non-self-adjoint boundary eigenvalue problems, the eigenvalues of which are highly sensitive to perturbations. We apply the algorithm to: the Orr–Sommerfeld equation with Poiseuille profile to prove the existence of an eigenvalue in the classically unstable region for Reynolds numberR=5772.221818; the Orr–Sommerfeld equation with Couette profile to prove upper bounds for the imaginary parts of all eigenvalues for fixedRand wave numberα; the problem of natural oscillations of an incompressible inviscid fluid in the neighbourhood of an elliptical flow to obtain information about the unstable part of the spectrum off the imaginary axis; Squire’s problem from hydrodynamics; and resonances of one-dimensional Schrödinger operators.

Linearization of boundary eigenvalue problems

1991 ◽  
Vol 14 (1) ◽  
pp. 105-119 ◽  
Author(s):  
Heinz Langer ◽  
Manfred M�ller
Keyword(s):  
Eigenvalue Problems ◽  
Boundary Eigenvalue
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