Blow-up and lifespan estimates of solutions to semilinear Moore–Gibson–Thompson equations. (December 2021) - Ming, Sen; Yang, Han; Fan, Xiongmei; Yao, Jiangyan
Abstract: In this paper, the blow-up of solutions to the Cauchy problems for semilinear Moore–Gibson–Thompson equations with power nonlinearity | u | p, derivative nonlinearity | u t | p, combined nonlinearity | u t | p + | u | q are investigated. Upper bound lifespan estimates of solutions to the problems in the sub-critical and critical cases are also deduced by applying the test function approach. It is worth noticing that blow-up results are valid in the conservative case. The main novelty is that the critical exponents in our cases are associated with the well-known Strauss exponent and Glassey exponent.