A blow – up result for the semilinear Moore – Gibson – Thompson equation with nonlinearity of derivative type in the conservative case

Abstract

In this paper, we study the blow-up of solutions to the semilinear Moore-Gibson-Thompson (MGT) equation with nonlinearity of derivative type |ut| p in the conservative case. We apply an iteration method in order to study both the subcritical case and the critical case. Hence, we obtain a blow-up result for the semilinear MGT equation (under suitable assumptions for initial data) when the exponent p for the nonlinear term satisfies 1 < p (n + 1)/(n − 1) for n 2 and p > 1 for n = 1. In particular, we find the same blow-up range for p as in the corresponding semilinear wave equation with nonlinearity of derivative type.

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

“…with β > 0, in the forthcoming paper [4], we shall study the blow -up of local in time solutions to (57) and the corresponding lifespan estimates under suitable assumptions for initial data. More specifically, the blow -up in finite time of energy solutions to (57) is going to be proved providing that the power p of the nonlinearity satisfies 1 < p p Gla (n)…”

Nonexistence Results for Semi-Linear Moore-Gibson-Thompson Equation With Non Local Operator

“…for the small initial data and low space dimensions 2 ≤ n ≤ 4 by using the energy estimates. Last years, the Moore-Gibson-Thompson (MGT) equation, a linearization of a model for wave propagation in viscous thermally relaxing uids has been studied by several authors (see [14], [6], [7], [16], [8], [17] and references therein). This model is realized through the third order hyperbolic partial dierential equation…”

The Galerkin Method for Fourth-Order Equation of the Moore–Gibson–Thompson Type with Integral Condition

“…The derivation of the equation, based on continuum and fluid mechanics, takes into account vis-cosity and heat conductivity as well as effect of the radiation of heat on the propagation of sound. The original derivation dates back to [44]. This model is realized through the thirdorder hyperbolic equation:…”

“…Besides, the coefficient b = βc 2 is related to the diffusively of the sound with β ∈ ð0, τ. In [44], Chen and Palmieri studied the blow-up result for the semilinear Moore-Gibson-Thompson equation with nonlinearity of derivative type in the conservative case defined as follows:…”