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(Usually one-parameter) semigroups of linear operators and their applications to partial differential equations, stochastic processes such as Markov processes and other branches of mathematics.

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Second order non-instantaneous impulsive evolution equations

The first order linear non-instantaneous impulsive evolution equations is given as; $$u'(t)=Au(t)~~ t\in[s_i,t_{i+1}],\,i\in\mathbb{N_0}:=\{0,1,2,...\}$$ $$u(t_i^+)=(E+B_i)u(t_i^-),\,\,i\in\mathbb{ …