Publikation: Strong and Mild Extrapolated $L^{2}$-Solutions to the Heat Equation with Constant Delay
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2015
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SIAM Journal on Mathematical Analysis. 2015, 47(1), pp. 427-454. ISSN 0036-1410. eISSN 1095-7154. Available under: doi: 10.1137/130937111
Zusammenfassung
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.
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510 Mathematik
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KHUSAINOV, Denys, Michael POKOJOVY, Reinhard RACKE, 2015. Strong and Mild Extrapolated $L^{2}$-Solutions to the Heat Equation with Constant Delay. In: SIAM Journal on Mathematical Analysis. 2015, 47(1), pp. 427-454. ISSN 0036-1410. eISSN 1095-7154. Available under: doi: 10.1137/130937111BibTex
@article{Khusainov2015Stron-40102,
year={2015},
doi={10.1137/130937111},
title={Strong and Mild Extrapolated $L^{2}$-Solutions to the Heat Equation with Constant Delay},
number={1},
volume={47},
issn={0036-1410},
journal={SIAM Journal on Mathematical Analysis},
pages={427--454},
author={Khusainov, Denys and Pokojovy, Michael and Racke, Reinhard}
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