For a class of semilinear elliptic systems, the existence of a broader class of multibump solutions is established under considerably weaker conditions than in earlier works. The key tool is the use ...of variational methods.
This paper studies a Hamiltonian system possessing a double well potential for which the existence of multitransition heteroclinic and homoclinic solutions that are local minimizers of an associated ...functional is known. Under an additional mild non-degeneracy condition on the set of all homoclinic and heteroclinic solutions, the existence of further heteroclinic and homoclinic solutions that are of mountain pass type is established. A key tool for the existence arguments is a variant of the Mountain Pass Theorem that is of independent interest.
On a phase transition model Byeon, Jaeyoung; Rabinowitz, Paul H.
Calculus of variations and partial differential equations,
05/2013, Letnik:
47, Številka:
1-2
Journal Article
Recenzirano
An Allen–Cahn phase transition model with a periodic nonautonomous term is presented for which an infinite number of transition states is shown to exist. A constrained minimization argument and the ...analysis of a limit problem are employed to get states having a finite number of transitions. A priori bounds and an approximation procedure give the general case. Decay properties are also studied and a sharp transition result with an arbitrary interface is proved.
This monograph presents extensions of the Moser-Bangert approach that include solutions of a family of nonlinear elliptic PDEs on Rn and an Allen-Cahn PDE model of phase transitions. The text may be ...used as a text for a graduate course in PDEs.
We combine the sensitivity advantages of cavity ring-down spectroscopy (CRDS) with the versatility of optical fiber sensing technology in a spatially extended passive fiber ring resonator constructed ...of common telecommunications components. The resonator is characterized with both pulsed and continuous-wave diode laser excitation, and it is shown to be a practical device for direct measurement of loss in a fiber-optic system as well for CRDS sensing in liquids. We demonstrate a minimum detectable loss of 0.017% per √Hz and show near-infrared absorption of 1-octyne with a minimum detectable concentration of 0.049% per √Hz in non-interacting solvent at 1532.5 nm.
PDF
