In this paperhttps://www.researchgate.net/publication/269404928_Periodic_solutions_for_nonlinear_evolution_equations_with_non-instantaneous_impulses authors prove the existence and stability of the solutions of the following first order linear non-instantaneous impulsive evolution equation:
$u'(t)=Au(t)~~ t\in[s_i,t_{i+1}],\,i\in\mathbb{N_0}:=\{0,1,2,...\}$
$u(t_i^+)=(E+B_i)u(t_i^-),\,\,i\in\mathbb{N}:=\{1,2,...\},$
$u(t)=(E+B_i)u(t_i^-),\,\, t\in(t_i,s_i],\,\, i\in\mathbb{N},$
$u(s_i^+)=u(s_i^-),\,\, i\in\mathbb{N}$
where $A:D(A)\subseteq X\rightarrow X$ is the Generator of a $C_0$-semigroup $\{T(t)\}_{t\geq 0}$ on a Banach space $X$ with a norm $\|.\|,\,B_i:X\rightarrow X,\,i\in\mathbb{N}$ is bounded linear operator,the sequences $\{s_i\}_{i\in\mathbb{N_0}}$ and $\{t_i\}_{i\in\mathbb{N_0}}$ are satisfied with the relation $t_i<s_i<t_{i+1},\,i\in\mathbb{N}$ and set $t_o=s_0=0$. Moreover $E$ denotes the standard identity.
Now, I am motivated to learn about the physical phenomena which can be described by this mathematical model. Therefore, please guide me to the literature where I can find the application of the above mentioned system of non-instantaneous impulsive evolution equations.
