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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Two vector Wiener-Hopf equations with 2x2 kernels containing oscillatory terms

## Two vector Wiener-Hopf equations with 2x2 kernels containing oscillatory termsAdd to your list(s) Download to your calendar using vCal - Pavlos Livasov (Aberystwyth University)
- Friday 16 August 2019, 12:00-12:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact info@newton.ac.uk. WHTW01 - Factorisation of matrix functions: New techniques and applications In the first part we discuss a steady-state problem for an interface crack between two dissimilar elastic materials. We consider a model of the process zone described by imperfect transmission conditions that reflect the bridging effect along a finite part of the interface in front of the crack. By means of Fourier transform, the problem is reduced into a Wiener-Hopf equation with a 2×2 matrix, containing oscillatory terms. We factorize the kernel following an existing numerical method and analyse its performance for various parameters of the problem. We show that the model under consideration leads to the classic stress singularity at the crack tip. Finally, we derive conditions for the existence of an equilibrium state and compute admissible length of the process zone. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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