TY - JOUR
T1 - Short time asymptotic behavior for parabolic equations
AU - Kannai, Yakar
PY - 1981/1/1
Y1 - 1981/1/1
N2 - We study the asymptotic behavior, off the diagonal, as t→0, of the fundamental solution of a second order parabolic equation, and obtain by analytic methods both local and global results. We treat both the fundamental solution of the Cauchy problem and that of some mixed initial boundary value problems. We also investigate the oscillatory behavior, off the diagonal, as λ→∞, of the spectral function of a higher order elliptic operator. Some open problems are also exhibited.
AB - We study the asymptotic behavior, off the diagonal, as t→0, of the fundamental solution of a second order parabolic equation, and obtain by analytic methods both local and global results. We treat both the fundamental solution of the Cauchy problem and that of some mixed initial boundary value problems. We also investigate the oscillatory behavior, off the diagonal, as λ→∞, of the spectral function of a higher order elliptic operator. Some open problems are also exhibited.
UR - http://www.scopus.com/inward/record.url?scp=0346125251&partnerID=8YFLogxK
U2 - 10.1016/s0304-0208(08)71105-8
DO - 10.1016/s0304-0208(08)71105-8
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AN - SCOPUS:0346125251
SN - 0304-0208
VL - 47
SP - 117
EP - 132
JO - North-Holland Mathematics Studies
JF - North-Holland Mathematics Studies
IS - C
ER -