HartungGorre Verlag
Inh.: Dr. Renate Gorre D78465 Konstanz Fon: +49 (0)7533 97227 Fax: +49 (0)7533 97228 www.hartunggorre.de 
S

Buğra Kabil
Analysis of
LiquidVapor
Interfaces
and Periodic Waves in
Dynamical
Lattice Systems
Konstanz 2016; 148
pages, EUR 64,00.
ISBN
9783866285637
The aim of this thesis is the analytical investigation
of liquidvapor interfaces and periodic traveling waves in dynamical lattice
systems. This work consists of two parts. The first part is the main part of
this work and deals with the analysis of the stability and the persistence of
liquidvapor interfaces in a multidimensional Van der Waals fluid. The subsonic
phase boundary is considered as a sharp free boundary connecting liquid and
vapor bulk phase dynamics given by the isothermal Euler equations. Surface
tension and configurational forces in the form of a kinetic relation determine
the evolution of the interface. The system of equations and trace conditions
are linearized so that we obtain a generalized hyperbolic initial boundary
value problem with higherorder boundary conditions. Linearization about a
nonconstant reference state results in a linear system with variable
coefficients. Stability and global existence theorems for the linearized system
with constant coefficients and also for the variable system are shown. By using
the results of these linearized systems, an iteration scheme yields the local
existence of solutions to the fully nonlinear problem which is stated as the
main result of this part in Theorem 5.4. The second part of this thesis
concerns the analysis of periodic traveling waves in dynamical lattice systems.
Three classes of nonlinear lattice systems resulting from spatial
discretization of partial differential equations are considered. We analyze the
stability of periodic traveling waves in these lattice systems. First, we
derive the socalled modulated equations (or Whitham
equations). Then, we investigate the spectral stability in a more analytical framework.
The major issue of this part is to give the link between the modulated
equations to the stability at the spectral level. We receive that modulation
theory is indeed related to spectral stability of periodic traveling waves. In
particular, we obtain that the characteristic speeds of the modulated equations
have to be real. The main result is given for the reactiondiffusion type
lattice system and stated in Theorem 5.1.
Keywords: liquidvapor interface, initial boundary value problem, hyperbolic
problem, local existence, undercompressive shock,
surface tension, kinetic relation, KreissLopatinskii
condition
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