Type of Publication:  Working Paper/Technical Report 
URI (citable link):  http://nbnresolving.de/urn:nbn:de:bsz:352244203 
Author:  Khusainov, Denys; Pokojovy, Michael; Racke, Reinhard 
Year of publication:  2013 
Series:  Konstanzer Schriften in Mathematik ; 320 
Summary: 
We propose a Hilbert space solution theory for a nonhomogeneous heat equation with delay in the highest order derivatives with nonhomogeneous Dirichlet boundary conditions in a bounded domain. Under rather weak regularity assumptions on the data, we prove a wellposedness result and give an explicit representation of solutions. Further, we prove an exponential decay rate for the energy in the dissipative case. We also show that lower order regularizations lead to illposedness, also for higherorder equations. Finally, an application with physically relevant constants is given.

Subject (DDC):  510 Mathematics 
Keywords:  delay equation 
Link to License:  Terms of use 
Bibliography of Konstanz:  Yes 
KHUSAINOV, Denys, Michael POKOJOVY, Reinhard RACKE, 2013. Strong and Mild Extrapolated L^{2}Solutions to the Heat Equation with Constant Delay
@techreport{Khusainov2013Stron24420, series={Konstanzer Schriften in Mathematik}, title={Strong and Mild Extrapolated L^{2}Solutions to the Heat Equation with Constant Delay}, year={2013}, number={320}, author={Khusainov, Denys and Pokojovy, Michael and Racke, Reinhard} }
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