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

Kenji Nishihara

    研究成果: Conference contribution

    1 引用 (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.

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

    Fingerprint

    Damped Wave Equation
    Semilinear Wave Equation
    Critical Exponents
    Damping
    Global Existence
    Dependent
    Exponent
    Semilinear
    Existence of Solutions
    Term

    ASJC Scopus subject areas

    • Mathematics(all)

    これを引用

    Nishihara, K. (2013). Critical exponent for the semilinear wave equation with time or space dependent damping. : Springer Proceedings in Mathematics and Statistics (巻 44, pp. 239-259). Springer New York LLC. https://doi.org/10.1007/978-3-319-00125-8_11

    Critical exponent for the semilinear wave equation with time or space dependent damping. / Nishihara, Kenji.

    Springer Proceedings in Mathematics and Statistics. 巻 44 Springer New York LLC, 2013. p. 239-259.

    研究成果: Conference contribution

    Nishihara, K 2013, Critical exponent for the semilinear wave equation with time or space dependent damping. : Springer Proceedings in Mathematics and Statistics. 巻. 44, Springer New York LLC, pp. 239-259. https://doi.org/10.1007/978-3-319-00125-8_11
    Nishihara K. Critical exponent for the semilinear wave equation with time or space dependent damping. : Springer Proceedings in Mathematics and Statistics. 巻 44. Springer New York LLC. 2013. p. 239-259 https://doi.org/10.1007/978-3-319-00125-8_11
    Nishihara, Kenji. / Critical exponent for the semilinear wave equation with time or space dependent damping. Springer Proceedings in Mathematics and Statistics. 巻 44 Springer New York LLC, 2013. pp. 239-259
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