Positivity and stability for some partial functional differential equations
The paper deals with the following partial functional-differential equation \[ u^\prime(t) = Bu(t) + F(u_t), \;t \geq 0, \] \[ u_0 = \varphi \in C([-r,0];X), \] where \(u_t (\theta) = u(t+\theta)\) for \(\theta \in [-r,0]\) and \(B\) is a non-densely defined linear operator satisfying the Hille-Yosida condition. The authors find necessary and sufficient conditions independent of the delay for the uniform exponential stability of the solution semigroup.
partial functional differential equations
scientific article; zbMATH DE number 1971895