The σ$$ \sigma $$‐evolution equations with friction and unbounded coefficients

We present in this article the study on decay estimates for solutions of Cauchy problem a class linear ‐evolution equations with unbounded coefficients space dimension , where coefficient is continuous and satisfying asymptotic behavior as parameter positive bounded function. By investigating diffusion phenomenon, we obtain new results that generalize our previous damped wave models constant nearly coefficients. Using solution problem, establish result global (in time) existence small data corresponding semilinear nonlinearity power type.