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

Kenji Nishihara

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    1 Citation (Scopus)

    Abstract

    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.

    Original languageEnglish
    Title of host publicationSpringer Proceedings in Mathematics and Statistics
    PublisherSpringer New York LLC
    Pages239-259
    Number of pages21
    Volume44
    ISBN (Print)9783319001241
    DOIs
    Publication statusPublished - 2013

    Fingerprint

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

    Keywords

    • Critical exponent
    • Damped wave equation
    • Diffusion phenomenon

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Nishihara, K. (2013). Critical exponent for the semilinear wave equation with time or space dependent damping. In Springer Proceedings in Mathematics and Statistics (Vol. 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. Vol. 44 Springer New York LLC, 2013. p. 239-259.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Nishihara, K 2013, Critical exponent for the semilinear wave equation with time or space dependent damping. in Springer Proceedings in Mathematics and Statistics. vol. 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. In Springer Proceedings in Mathematics and Statistics. Vol. 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. Vol. 44 Springer New York LLC, 2013. pp. 239-259
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