Blow‐up and lifespan estimates of solutions to the weakly coupled system of semilinear Moore–Gibson–Thompson equations. (9th May 2021)

• Record Type: Journal Article
• Authors: Ming, Sen; Yang, Han; Fan, Xiongmei
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 14(2021)
• Page Start: 10972
• Page End: 10992
• Publication Date: 2021-05-09
• Subjects: lifespan estimates -- semilinear Moore–Gibson–Thompson equations -- test function technique -- weakly coupled system; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7462
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This work is devoted to investigating formation of singularities of solutions to the weakly coupled system of semilinear Moore–Gibson–Thompson equations with power nonlinearities | v | p, | u | q, derivative nonlinearities | v t | p, | u t | q, mixed nonlinearities | v | q, | u t | p, and combined nonlinearities | v t | p 1 + | v | q 1, | u t | p 2 + | u | q 2, respectively. Upper bound lifespan estimates of solutions to the problem in the subcritical and critical cases are also established. The main tool employed in the proofs is test function technique. The novelty is that lifespan estimates of solutions are connected with the well‐known Strauss exponent and Glassey exponent.