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Asymptotic behavior of solutions of the mixed problem for semilinear hyperbolic equations
We discuss the optimality of the decay
estimate of the mixed problem (MP) for semilinear hyperbolic equations
of the type of the Euler-Poisson-Darboux equation. For this purpose
we investigate decay properties and the lower bounds of the
solutions to a boundary value problem related to (MP) as $t
\rightarrow \infty $.