Article ID: MTJPAM-D-21-00043

Title: Nonexistence of global weak solutions of semilinear degenerate hyperbolic equation of the second kind


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-21-00043; Volume 4 / Issue 2 / Year 2022, Pages 28-36

Document Type: Research Paper

Author(s): Kangqun Zhang a

aDepartment of Mathematics and Physics, Nanjing Institute of Technology, Nanjing, 211167, China

Received: 16 June 2021, Accepted: 14 April 2022, Published: 27 May 2022.

Corresponding Author: Kangqun Zhang (Email address: chkqnju@hotmail.com)

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Abstract

In the present paper, we investigate the existence of weak solutions of semilinear degenerate hyperbolic equation of the second kind in C1((0, T),Lp(Ω)) for any p ∈ [1, +∞], n ∈ ℤ+. Our approach is based on analyzing the first Fourier coefficient of solution to establish a scope of lifespan. Finally, we obtain nonexistence of global weak solution of a semilinear hyperbolic equation of the second kind with positive initial data.

Keywords: Hyperbolic equation, characteristic degeneration, the first Fourier coefficient, test function, nonexistence

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