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  • 1
    Electronic Resource
    Electronic Resource
    Existence theory for damped gravity waves in a closed rectangular basin (1991)
    Springer
    Archive for rational mechanics and analysis 114 (1991), S. 267-295 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study existence and uniqueness of solutions of the equations for the free surface motion of an incompressible, irrotational fluid in a rectangular basin subject to vertical oscillation. After adding artificial damping, which leaves the flow irrotational but correctly represents the physical rate of energy loss at high wave numbers, we prove global existence and uniqueness results in the appropriate Sobolev spaces, provided that the initial data and forcing amplitudes have sufficiently small norms. Convergence of spatially discretized (finite-dimensional) projections is also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00385972
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Twisted and nontwisted bifurcations induced by diffusion (1996)
    Springer
    Journal of dynamics and differential equations 8 (1996), S. 325-372 
    Details
    ISSN: 1572-9222
    Keywords: Reaction-diffusion equations ; predator-prey systems ; homoclinic bifurcations ; periodic solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop. When the diffusion coefficients are large, this solution represents a stable, spatially homogeneous time-periodic solution of the PDE. We show that when the diffusion coefficients become small, the spatially homogeneous periodic solution becomes unstable and bifurcates into spatially nonhomogeneous periodic solutions. The nature of the bifurcation is determined by the twistedness of an equilibrium/homoclinic bifurcation that occurs as the diffusion coefficients decrease. In the nontwisted case two spatially nonhomogeneous simple periodic solutions of equal period are generated, while in the twisted case a unique spatially nonhomogeneous double periodic solution is generated through period-doubling.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02218759
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Transition layers for singularly perturbed delay differential equations with monotone nonlinearities (1989)
    Springer
    Journal of dynamics and differential equations 1 (1989), S. 3-43 
    Details
    ISSN: 1572-9222
    Keywords: Differential delay equations ; singular perturbations ; transition layers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Transition layers arising from square-wave-like periodic solutions of a singularly perturbed delay differential equation are studied. Such transition layers correspond to heteroclinic orbits connecting a pair of equilibria of an associated system of transition layer equations. Assuming a monotonicity condition in the nonlinearity, we prove these transition layer equations possess a unique heteroclinic orbit, and that this orbit is monotone. The proof involves a global continuation for heteroclinic orbits.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01048789
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Symbolic dynamics and nonlinear semiflows (1986)
    Springer
    Annali di matematica pura ed applicata 144 (1986), S. 229-259 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary For a transverse homoclinic orbit γ of a mapping (not necessarily invertible) on a Banach space, it is shown that the mapping restricted to orbits near γ is equivalent to the shift automorphism on doubly infinite sequences on finitely many symbols. Implications of this result for the Poincaré map of semiflows are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01760821
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    Paper (German National Licenses)
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