• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.773-786
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• 2023

In this paper, we introduce the pseudospectra of bounded linear operators on quasi normed space and study its proprieties. Beside that, we establish the relationship between the pseudospectra of a sequence of bounded linear operators and its limit.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.691-694
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• 2002

The most unstable situation of laminar plane Poiseuille flow for transition to turbulence is investigated by using a pseudo-spectral method. A number of various disturbance modes are tested and it is found that the flow is the most unstable when it is disturbed by an oblique wave with an angle of $29.7^{\circ}$.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.3
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• pp.319-325
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• 2003

We investigate the spectra and the pseudospectra in plane Poiseuille flow, plane Couette flow and Blasius flow. At subcritical Reynolds number, the spectra are lied strictly inside the stable complex half-plane, but the pseudospectra are lied in the unstable half-plane, reflecting the large linear transient growth that certain perturbations may excite. It means that the smooth flows may become to turbulent even though all the eigenmodes decay monotonically. We found that pseudospectra is one reason that causes subcritical transition in plane Poiseuille flow and plane Couette flow and bypass transition in Blasius flow.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.673-697
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• 2020

In this paper, we introduce and study the structured essential approximate and defect pseudospectrum of closed, densely defined linear operators in a Banach space. Beside that, we discuss some results of stability and some properties of these essential pseudospectra. Finally, we will apply the results described above to investigate the essential approximate and defect pseudospectra of the following integro-differential transport operator.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.6
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• pp.766-772
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• 2003

The pseudospectral method for stability analysis was used to find the most influential disturbance mode for transition of plane channel flows and Blasius flow at their critical Reynolds numbers. A number of various oblique disturbance waves were investigated for their pseudospectra and resolvent norm contours in each flow, and an exhaustive search method was employed to find the disturbing waves to which the flows become most unstable. In plane Poiseuille flow an oblique disturbance with a wavelength of 3.59h (where h is the half channel width) at an angle $28.7^{\circ}$ was found to be the most influential for the flow transition to turbulence, and in plane Couette flow it is an oblique wave with a wavelength of 3.49h at an angle of $19.4^{\circ}$. But in Blasius flow it was found that the most influential mode is a normal wave with a wavelength of $3.44{\delta}_{999}$. These results imply that the most influential disturbance mode is closely related to the fundamental acoustic wave with a certain shear sheltering in the respective flow geometry.