Abstract
We study the Cauchy problem of the semilinear damped wave equation in one space dimension. We show the existence of global solutions in the critical case with small initial data in weighted L 2-spaces. This problem in multidimensional cases was dealt with in Sobajima (Differ Integr Equ 32:615–638, 2019) via the weighted Hardy inequality which is false in one-dimension. The crucial idea of the proof is the use of an incomplete version of Hardy inequality.
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Sobajima, M., Wakasugi, Y. (2021). Remark on One Dimensional Semilinear Damped Wave Equation in a Critical Weighted L 2-space. In: Ferone, V., Kawakami, T., Salani, P., Takahashi, F. (eds) Geometric Properties for Parabolic and Elliptic PDE's. Springer INdAM Series, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-030-73363-6_14
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DOI: https://doi.org/10.1007/978-3-030-73363-6_14
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