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Semilinear viscous Moore-Gibson-Thompson equation with the derivative-type nonlinearity: Global existence versus blow-up
AIMS Mathematics 2022, 7(1): 247-257
Published: 15 January 2022
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In this paper, we study global existence and blow-up of solutions to the viscous Moore-Gibson-Thompson (MGT) equation with the nonlinearity of derivative-type | u t | p . We demonstrate global existence of small data solutions if p > 1 + 4 / n ( n 6) or p 2 2 / n ( n 7), and blow-up of nontrivial weak solutions if 1 < p 1 + 1 / n. Deeply, we provide estimates of solutions to the nonlinear problem. These results complete the recent works for semilinear MGT equations by [4].

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