Critical exponent for the semilinear wave equation with time or space dependent damping

Kenji Nishihara*

*この研究の対応する著者

    研究成果: Conference contribution

    1 被引用数 (Scopus)

    抄録

    Since the damped wave equation has the diffusion phenomenon, the critical exponent is expected to be the same as that for the corresponding diffusive equation with semilinear term. Therefore, we first remember the basic facts on the diffusion phenomenon. Then, from this point of view, we can conjecture the critical exponent for the damped wave equation and state several results. Finally, the small data global existence of solutions is shown in the supercritical exponent, while no global existence for some data is done in the critical and subcritical exponents. The latter part will be applied to the semilinear damped wave equation with quadratically decaying potential.

    本文言語English
    ホスト出版物のタイトルSpringer Proceedings in Mathematics and Statistics
    出版社Springer New York LLC
    ページ239-259
    ページ数21
    44
    ISBN(印刷版)9783319001241
    DOI
    出版ステータスPublished - 2013

    ASJC Scopus subject areas

    • 数学 (全般)

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