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

Kenji Nishihara*

*Corresponding author for this work

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

    1 Citation (Scopus)


    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
    Number of pages21
    ISBN (Print)9783319001241
    Publication statusPublished - 2013


    • Critical exponent
    • Damped wave equation
    • Diffusion phenomenon

    ASJC Scopus subject areas

    • Mathematics(all)


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