Well-posedness and Energy Decay of Solutions to a Coupled System of Heat and Schr\"{o}dinger Equations.
DOI:
https://doi.org/10.2298/FIL2609225BKeywords:
Uniqueness, $C_0$-Semigroup, Frequency domain approach, Analyticity of semigroups, Operators of fractional order.Abstract
Our goal is to examine a system of a Schr\"{o}dinger equation coupled with a heat equation in a bounded region. The coupling involves an operator that is parameterized by a real number in [0,1]. For $0\leq \theta<1$, we show that the associated semigroup of the system is not exponentially stable. We then propose a specific non-uniform decay rate. When $\theta= 1$, the linked semigroup is exponentially stable rather than analytic.
