BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Partial Differential Equations seminar
SUMMARY:Boundary kernels for dissipative systems - Shih-Hs
ien Yu (Singapore)
DTSTART;TZID=Europe/London:20120423T160000
DTEND;TZID=Europe/London:20120423T170000
UID:TALK36073AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/36073
DESCRIPTION:In this talk we will present a study on the kernel
functions of the Dirichlet-‐Neumann maps for dis
sipative systems in a half space. We start from th
e consideration of the Green’s function for an ini
tial-‐boundary value problems for linear dissipat
ive systems. With the fundamental solutions of the
dissipative systems\, one can reduce the initial-
‐boundary value problems into boundary value prob
lems so that the well-‐posedness of the system gi
ves linear algebraic systems over the polynomials
in the Fourier and Laplace variables for the Diric
hlet-‐Neumann datum at the boundary\, where Fouri
er variables are in the directions of boundary\, a
nd the Laplace is for the time variable.\n\nIn ord
er to invert the Dirichlet-‐Neumann map from the
transformation variables to the space-‐time varia
bles we introduce a path\, which contains the spec
tral information of the systems\, in the complex p
lan for the time Laplace variable. On this path\,
the Laplace-‐Fourier variables can be recombined\
, through the Cauchy’s complex contour integral\,
into a form resemble to that for a whole space pro
blem. Thus\, the classical results for the whole s
pace problem can be used to obtain the pointwise s
pae-‐time structure for long wave components of t
he kernel function of the Dirichlet-‐Neumann map
for points within a finite Mach region. We also ap
ply direct energy estimates to yield the pointwise
structure of the kernel functions in any high Mac
h number region. Finally\, we have obtained expone
ntially sharp estimates for the kernel function in
the space-‐time variables. For example\, the ker
nel functions for both D’Alermbert wave equation w
ith dissipation and a linearized compressible Navi
er-‐Stokes equation can be expressed explicitly i
n space-‐time variables with errors which decay e
xponentially in both space-‐time variables. This
gives a globally quantitative and qualitative wave
propagations at boundary.
LOCATION:CMS\, MR15
CONTACT:Jonathan Ben-Artzi
END:VEVENT
END:VCALENDAR