Longtime behavior of small solutions to viscous perturbations of nonlinear hyperbolic systems in 3D
- Degree Grantor:
- University of California, Santa Barbara. Mathematics
- Degree Supervisor:
- Thomas C. Sideris
- Place of Publication:
- [Santa Barbara, Calif.]
- Publisher:
- University of California, Santa Barbara
- Creation Date:
- 2014
- Issued Date:
- 2014
- Topics:
- Mathematics
- Keywords:
- Partial,
Equations,
Differential,
Hyperbolic,
Perturbations, and
Nonlinear - Genres:
- Online resources and Dissertations, Academic
- Dissertation:
- Ph.D.--University of California, Santa Barbara, 2014
- Description:
The first result in this dissertation concerns wave equations in three space dimensions with small O(nu) viscous dissipation and O(delta) non-null quadratic nonlinearities. Small O(epsilon) solutions are shown to exist globally provided that epsilondelta/nu is sufficiently small. When this condition is not met, small solutions exist almost globally, and in certain parameter ranges, the addition of dissipation enhances the lifespan. We study next a system of nonlinear partial differential equations modeling the motion of incompressible Hookean isotropic viscoelastic materials. The nonlinearity inherently satisfies a null condition and our second result establishes global solutions with small initial data independent of viscosity. In the proofs we use vector fields, energy estimates, and weighted decay estimates.
- Physical Description:
- 1 online resource (126 pages)
- Format:
- Text
- Collection(s):
- UCSB electronic theses and dissertations
- Other Versions:
- http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:3645652
- ARK:
- ark:/48907/f31v5c3h
- ISBN:
- 9781321349603
- Catalog System Number:
- 990045117150203776
- Copyright:
- Boyan Jonov, 2014
- Rights:
- In Copyright
- Copyright Holder:
- Boyan Jonov
File | Description |
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Access: Public access | |
Jonov_ucsb_0035D_12313.pdf | pdf (Portable Document Format) |