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Decay/growth rates for inhomogeneous heat equations with memory. The case of large dimensions

  • Received: 17 April 2021 Accepted: 07 July 2021 Published: 09 August 2021
  • We study the decay/growth rates in all $ L^p $ norms of solutions to an inhomogeneous nonlocal heat equation in $ \mathbb{R}^N $ involving a Caputo $ \alpha $-time derivative and a power $ \beta $ of the Laplacian when the dimension is large, $ N > 4\beta $. Rates depend strongly on the space-time scale and on the time behavior of the spatial $ L^1 $ norm of the forcing term.

    Citation: Carmen Cortázar, Fernando Quirós, Noemí Wolanski. Decay/growth rates for inhomogeneous heat equations with memory. The case of large dimensions[J]. Mathematics in Engineering, 2022, 4(3): 1-17. doi: 10.3934/mine.2022022

    Related Papers:

  • We study the decay/growth rates in all $ L^p $ norms of solutions to an inhomogeneous nonlocal heat equation in $ \mathbb{R}^N $ involving a Caputo $ \alpha $-time derivative and a power $ \beta $ of the Laplacian when the dimension is large, $ N > 4\beta $. Rates depend strongly on the space-time scale and on the time behavior of the spatial $ L^1 $ norm of the forcing term.



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