We investigate asymptotic property of the solution to the boundary value problem (BV) for the semilinear Euler-Poisson-Darboux type equation as t tends to infinity. Applying this result to the boundary value problem of the semilinear wave equation with a nonlinear dissipation we show the optimality of the decay estimate. Also we discuss the optimality of the decay estimates and lower bounds of solutions the mixed problem corresponding to (BV). [References: 8]
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