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2019 | OriginalPaper | Chapter

The Cauchy Problem for Dissipative Wave Equations with Weighted Nonlinear Terms

Authors : Makoto Nakamura, Hidemitsu Wadade

Published in: New Tools for Nonlinear PDEs and Application

Publisher: Springer International Publishing

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Abstract

The Cauchy problem for dissipative wave equations with weighted nonlinear terms is considered. The nonlinear terms are power type with a singularity at the origin of Coulomb type. The local and global solutions are shown in the energy class by the use of the Caffarelli-Kohn-Nirenberg inequality. The exponential type nonlinear terms are also considered in the critical two-spatial dimensions.

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previous chapter Smoothing and Strichartz Estimates to Perturbed Magnetic Klein-Gordon Equations in Exterior Domain and Some Applications

next chapter Global Existence Results for a Semilinear Wave Equation with Scale-Invariant Damping and Mass in Odd Space Dimension

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Title: The Cauchy Problem for Dissipative Wave Equations with Weighted Nonlinear Terms
Authors: Makoto Nakamura
Hidemitsu Wadade
Publisher: Springer International Publishing
Book: New Tools for Nonlinear PDEs and Application
Print ISBN: 978-3-030-10936-3

Electronic ISBN: 978-3-030-10937-0

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-030-10937-0_11

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