On the spectral properties of the Bloch–Torrey equation in infinite periodically perforated domains

  • Denis S. Grebenkov

    École Polytechnique, Palaiseau, France
  • Bernard Helffer

    Université de Nantes, France
  • Nicolas Moutal

    École Polytechnique, Palaiseau, France
On the spectral properties of the Bloch–Torrey equation in infinite periodically perforated domains cover

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Abstract

We investigate spectral and asymptotic properties of the particular Schrödinger operator (also known as the Bloch–Torrey operator), , in infinite periodically perforated domains of . We consider Dirichlet realizations of this operator and formalize a numerical approach proposed in [17] for studying such operators. In particular, we discuss the existence of the spectrum of this operator and its asymptotic behavior as .