[Turkmath:7520] Bogazici Univ Çarşamba seminerleri - ilan ekte

[ferit.ozturk at boun.edu.tr]

Geçmiş/gelecek konuşmalar için:
http://www.math.boun.edu.tr/index.php?option=com_content&task=section&id=49&Itemid=405

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BOGAZICI UNIVERSITY MATH COLLOQUIUM

Global existence and blow-up results for nonlocal
nonlinear wave equations

Husnu A. Erbay
Isık Universitesi

Date : Wednesday, March 16, 2011
Time: 14:00
Place: TB 250, Bogazici Universitesi

Abstract: In this talk, I will summarize our recent results obtained in [1-3]
for nonlocal nonlin-
ear wave equations. In those studies three different problems which model
longitudinal, transverse
and anti-plane shear motions, respectively, were considered and the
regularizing
effect of the nonlo-
cal behavior was discussed. In each case the wave equation involves a
convolution integral operator
with a general kernel function whose Fourier transform is nonnegative. Some
well-known exam-
ples of nonlinear wave equations are special cases of the present equations for
suitable choices of
the kernel function. We establish global existence of solutions of the
equations
assuming enough
smoothness on the initial data together with some positivity conditions on the
nonlinear term. Fur-
thermore, conditions for finite time blow-up are provided.
[1] N. Duruk, H.A. Erbay, A.Erkip, Global existence and blow-up for a class of
nonlocal nonlinear
Cauchy problems arising in elasticity, Nonlinearity 23, 107-118 (2010).
[2] N. Duruk, H.A. Erbay, A. Erkip, Blow-up and global existence for a general
class of nonlocal
nonlinear coupled wave equations, Journal of Differential Equations 250,
1448-1459 (2011).
[3] H.A. Erbay, S. Erbay, A. Erkip, The Cauchy problem for a class of
two-dimensional nonlocal
nonlinear wave equations governing anti-plane shear motions in elastic
materials, Nonlinearity (in
press).

Tea and coffee will be served at 15:00

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