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The corresponding evolution problem is: $$\\dot{u}=A(t)u+F(t,u)+b(t), \\quad t\\ge 0; \\quad u(0)=u_0. \\qquad (*)$$ Here $\\dot{u}:=\\frac {du}{dt}$, $u=u(t)\\in H$, $t\\in \\R_+:=[0,\\infty)$, $A(t)$ is a linear dissipative operator: Re$(A(t)u,u)\\le -\\gamma(t)(u,u)$, $\\gamma(t)\\ge 0$, $F(t,u)$ is a nonlinear operator, $\\|F(t,u)\\|\\le c_0\\|u\\|^p$, $p>1$, $c_0,p$ are constants, $\\|b(t)\\|\\le \\beta(t),$ $\\beta(t)\\ge 0$ is a continuous function. 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The corresponding evolution problem is: $$\\dot{u}=A(t)u+F(t,u)+b(t), \\quad t\\ge 0; \\quad u(0)=u_0. \\qquad (*)$$ Here $\\dot{u}:=\\frac {du}{dt}$, $u=u(t)\\in H$, $t\\in \\R_+:=[0,\\infty)$, $A(t)$ is a linear dissipative operator: Re$(A(t)u,u)\\le -\\gamma(t)(u,u)$, $\\gamma(t)\\ge 0$, $F(t,u)$ is a nonlinear operator, $\\|F(t,u)\\|\\le c_0\\|u\\|^p$, $p>1$, $c_0,p$ are constants, $\\|b(t)\\|\\le \\beta(t),$ $\\beta(t)\\ge 0$ is a continuous function. 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