A blow-up result for a semilinear wave equation with scale-invariant damping and mass and nonlinearity of derivative type

Nonexistence of global solutions for the semilinear Moore – Gibson – Thompson equation in the conservative case

“…Nonetheless, as in the subcritical case, we have to consider a sequence of parameters (cf. {Ω j } j∈N in Section 5) which characterizes the slicing procedure of the domain of integration that has a relatively different structure with respect to the one which is usually used to deal with critical cases [1,44,45,30,31,32,33].…”

A blow-up result for a Nakao-type weakly coupled system with nonlinearities of derivative-type

“…In our case, since we work with the weakly coupled system (1) together with d'Alembert's formula (coming from the equation for v) we shall also employ the representation formulas ( 15) and ( 16) from Section 3. Notice that (15) coincides exactly with (16) for µ = 0. Hence, in what follows we work always with (15) for both cases.…”

“…Recently, this approach have been applied to study semilinear models with time-dependent coefficients (cf. [16,12,9]).…”

A note on the nonexistence of global solutions to the semilinear wave equation with nonlinearity of derivative-type in the generalized Einstein-de Sitter spacetime

“…In the present section, we prove the main blowup results by using a generalization of Zhou's blow-up argument on the characteristic line A k (t)−z = R. In place of the d'Alembert's formula we shall employ the integral representation formulae from Theorems 1.1 and 1.2 obtained via Yagdjian's Integral Transform approach. The main steps in the proof are inspired by the computations in [29,18,10].…”

“…has a crucial role in determining some properties of the fundamental solution of L k,µ,ν 2 . In the special case k = 0 (the so-called wave operator with scale-invariant damping and mass), it is known in the literature that the value of δ affects not only the fundamental solution of L 0,µ,ν 2 but also the critical exponents in the treatment of semilinear Cauchy problem associated with L 0,µ,ν 2 with power nonlinearity [11,16,17,1], nonlinearity of derivative type [18], and combined nonlinearity [4,5].…”