Applications of Singular Perturbation Methods in the Mathematical Theory of
Viscoelasticity
Daniel Ševčovič
PhD thesis advisor:
Pavol Brunovský
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PhD thesis - Full text (PDF
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Summary:
Part I.
Spurt phenomenon for a non-Newtonian
model
of shearing motions including diffusion
2. Non-Newtonian model of shearing motions including diffusion
3. Existence of solutions, asymptotic behavior
and properties of steady states
3.1 Existence of solutions
3.2 Asymptotic behavior of solutions
3.3 Steady states
4. Spurt
5. Hysteresis
6. Numerical simulations
7. Discussion
Part II.
Singular limit dynamics of invariant manifolds and vector fields
8. Foreword
9. Preliminaries
9.2 Existence of solutions of a family of
abstract equations
9.3 Banach spaces with exponentially weighted
norms
10. Invariant manifolds
11. Applications
11.1 The limiting behavior of invariant
manifolds and global attractors
for a model of shearing motions
11.2 Applications to elastic systems with
structural damping