Work

Critical exponent for global solutions in a fourth‐order hyperbolic equation of p‐Kirchhoff type

Year: 2024

Type: article

Abstract: We study a fourth‐order hyperbolic equation involving Kirchhoff type ‐Laplacian and superlinear source, subject to zero Navier boundary condition, where is an open bounded domain in with ; denotes the maximal existence time; and and are constants. For , using auxiliary function method and Sobolev inequality, we prove that there are only global solutions. For , we obtain the optimal classification of initial energy and Nehari energy, which guarantees the existence of blow‐up solutions and global solutions. In the critical case , we find out that the coefficients of the Kirchhoff term and the superlinear source play important role in separating out the property of weak solutions.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.10438

Authors: Bingchen Liu, Jiaxin Dou

Institution: China University of Petroleum, East China

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Natural Science Foundation of China, Natural Science Foundation of Shandong Province

OpenAlex ID: W4401828058

FWCI: 0.781

Cites: 15

Cited by: 1

Related to: 10