Applications of Singular Perturbation Methods in the Mathematical Theory of Viscoelasticity
Daniel Ševčovič
PhD thesis advisor: Pavol Brunovský

PhD thesis - Full text    (PDF 730 K)

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