Abstract
We analyze the asymptotic behavior of solutions to wave equations with strong damping terms in $\textbf{R}^n$ $(n\ge1)$, $$ u_{tt}-\Delta u-\Delta u_t=0, \qquad u(0,x)=u_0(x), \quad u_t(0,x)=u_1(x). $$ If the initial data belong to suitable weighted $L^1$ spaces, lower bounds for the difference between the solutions and the leading terms in the Fourier space are obtained, which implies the optimality of expanding methods and some estimates proposed in [13] and in this paper.
Acknowledgment
The author would like to thank Professor Ryo Ikehata for fruitful discussions and warm encouragement. The author is also grateful to the referees for careful reading and useful suggestions.
Citation
Hironori MICHIHISA. "Optimal leading term of solutions to wave equations with strong damping terms." Hokkaido Math. J. 50 (2) 165 - 186, June 2021. https://doi.org/10.14492/hokmj/2018-920
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