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Strong and Mild Extrapolated L<sup>2</sup>-Solutions to the Heat Equation with Constant Delay

Strong and Mild Extrapolated L2-Solutions to the Heat Equation with Constant Delay

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KHUSAINOV, Denys, Michael POKOJOVY, Reinhard RACKE, 2013. Strong and Mild Extrapolated L2-Solutions to the Heat Equation with Constant Delay

@techreport{Khusainov2013Stron-24420, series={Konstanzer Schriften in Mathematik}, title={Strong and Mild Extrapolated L2-Solutions to the Heat Equation with Constant Delay}, year={2013}, number={320}, author={Khusainov, Denys and Pokojovy, Michael and Racke, Reinhard} }

Khusainov, Denys 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 well-posedness 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 ill-posedness, also for higher-order equations. Finally, an application with physically relevant constants is given. 2013-09-24T08:59:24Z Pokojovy, Michael 2013 terms-of-use Racke, Reinhard 2013-09-24T08:59:24Z Khusainov, Denys Strong and Mild Extrapolated L<sup>2</sup>-Solutions to the Heat Equation with Constant Delay eng Racke, Reinhard Pokojovy, Michael

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