Local existence and nonexistence for fractional in time weakly coupled reaction-diffusion systems

Masamitsu Suzuki ()
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Masamitsu Suzuki: The University of Tokyo

Partial Differential Equations and Applications, 2021, vol. 2, issue 1, 1-27

Abstract: Abstract We study a fractional in time weakly coupled reaction-diffusion system in a bounded domain with the Dirichlet boundary condition. The domain is imbedded in an N-dimensional space and it has $$C^2$$ C 2 boundary, and fractional derivatives are meant in a generalized Caputo sense. The system can be referred to as a standard reaction-diffusion system in two components with polynomial growth. We obtain integrability conditions on the initial state functions which determine the existence/nonexistence of a local in time mild solution.

Keywords: Local in time solutions; Caputo fractional derivative; Singular initial functions; Uniqueness; Cauchy sequences; Semigroup estimates; Primary; 35K51; 35A01; 35R11; Secondary; 26A33; 46E35 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s42985-020-00061-9

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