Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • Articles: DFG German National Licenses  (2)
  • 1985-1989  (2)
Source
Material
Years
Year
  • 1
    Electronic Resource
    Electronic Resource
    A Poincaré-Bendixson theorem for scalar reaction diffusion equations (1989)
    Springer
    Archive for rational mechanics and analysis 107 (1989), S. 325-345 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract For scalar equations $$u_t = u_{xx} + f(x, u, u_x )$$ with x ε S 1 and f ε C 2 we show that the classical theorem of Poincaré and Bendixson holds: the ω-limit set of any bounded solution satisfies exactly one of the following alternatives: - it consists in precisely one periodic solution, or - it consists of solutions tending to equilibrium as $$t \to \pm \infty $$ This is surprising, because the system is genuinely infinite-dimensional.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00251553
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Global Hopf bifurcation of two-parameter flows (1986)
    Springer
    Archive for rational mechanics and analysis 94 (1986), S. 59-81 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The behavior of center-indices, as introduced by J. Mallet-Paret & J. Yorke, is analyzed for two-parameter flows. The integer sum of center-indices along a one-dimensional curve in parameter space is called the H-index. A nonzero H-index implies global Hopf bifurcation. The index H is not a homotopy invariant. This fact is due to the occurrence of stationary points with an algebraically double eigenvalue zero, which we call B-points. To each B-point we assign an integer B-index, such that the H-index relates to the B-indices by a formula such as occurs in the calculus of residues. This formula is easily applied to study global bifurcation of periodic solutions in diffusively coupled two-cells of chemical oscillators and to treat spatially heterogeneous time-periodic oscillations in porous catalysts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00278243
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...