Stability result for a variable-exponent viscoelastic double-Kirchhoff type inverse source problem with nonlocal degenerate damping term

Coupled system of nonlinear viscoelastic plate equations of (p(x),q(x))‐Kirchhoff‐type: Global existence, general decay, and blow‐up

“…Due to the great importance both theoretically and practically, numerous researchers have studied equations with nonstandard growth conditions, that is, equations with the variable exponent of nonlinearities, [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. Compared with equations with variable exponent nonlinearities, less work has been done in a system of equations with variable exponent nonlinearities.…”

Upper bounds for the blow up time for the Kirchhoff- type equation

“…Later, Li et al [10] proved the asymptotic stability of solutions (5). Recently, some other authors studied hyperbolic type equations with variable exponents (see [1,2,4,11,17,18,20,21]). Motivated by the above studies, in this work, we consider the upper bounds of blow up time of the solution (1) under suitable conditions.…”

Existence and Decay of Solutions for a Parabolic-Type Kirchhoff Equation with Variable Exponents

“…Recently, problems with variable exponents have been handled carefully in several papers, some results relating the local existence, global existence, blow up and stability have been found ([13]- [17]).…”