On the spectral properties of the Bloch–Torrey equation in infinite periodically perforated domains
Denis S. GrebenkovÉcole Polytechnique, Palaiseau, France
Bernard HelfferUniversité de Nantes, France
Nicolas MoutalÉcole Polytechnique, Palaiseau, France
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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  for studying such operators. In particular, we discuss the existence of the spectrum of this operator and its asymptotic behavior as .