The Cauchy Problem for Dissipative Wave Equations with Weighted Nonlinear Terms

Makoto Nakamura,Hidemitsu Wadade

doi:10.1007/978-3-030-10937-0_11

The Cauchy Problem for Dissipative Wave Equations with Weighted Nonlinear Terms

Makoto Nakamura, Hidemitsu Wadade

https://doi.org/10.1007/978-3-030-10937-0_11

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Publication Date: Jan 1, 2019

Affiliation: Yamagata University, Kanazawa University

#Nonlinear Terms #Exponential Nonlinear Terms + Show 8 more

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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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