Skip to main content
padlock icon - secure page this page is secure

Absolute and Convective Instability for Evolution PDEs on the Half-Line

Buy Article:

$59.00 + tax (Refund Policy)

We analyze evolution PDEs exhibiting absolute (temporal) as well as convective (spatial) instability. Let (k) be the associated symbol, i.e., let exp[ikx−(k)t] be a solution of the PDE. We first study the problem on the infinite line with an arbitrary initial condition q0(x) , where q0(x) decays as |x| → ∞ . By making use of a certain transformation in the complex k-plane, which leaves (k) invariant, we show that this problem can be analyzed in an elementary manner. We then study the problem on the half-line, a problem physically more realistic but mathematically more difficult. By making use of the above transformation, as well as by employing a general method recently introduced for the solution of initial-boundary value problems, we show that this problem can also be analyzed in a straightforward manner. The analysis is presented for a general PDE and is illustrated for two physically significant evolution PDEs with spatial derivatives up to second order and up to fourth order, respectively. The second-order equation is a linearized Ginzburg–Landau equation arising in Rayleigh–BĂ©nard convection and in the stability of plane Poiseuille flow, while the fourth-order equation is a linearized Kuramoto–Sivashinsky equation, which includes dispersion and which models among other applications, interfacial phenomena in multifluid flows.
No References
No Citations
No Supplementary Data
No Article Media
No Metrics

Document Type: Research Article

Affiliations: 1: University of Cambridge 2: New Jersey Institute of Technology

Publication date: January 1, 2005

  • Access Key
  • Free content
  • Partial Free content
  • New content
  • Open access content
  • Partial Open access content
  • Subscribed content
  • Partial Subscribed content
  • Free trial content
Cookie Policy
Cookie Policy
Ingenta Connect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more