Initial Boundary Value Problem for a Fractional Viscoelastic Equation of the Kirchhoff Type

Yang, Liu; Zhang, Li

doi:10.3390/fractalfract6100581

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2023

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“…Again, by (59), we obtain (57), which implies that ζ 1 < 0 and ζ 2 < 0. Thus, by (10), for all θ > 0, there holds…”

Section: Discussionmentioning

confidence: 95%

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A One-Dimensional Time-Fractional Damped Wave Equation with a Convection Term

2023

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We investigate a semilinear time-fractional damped wave equation in one dimension, posed in a bounded interval. The considered equation involves a convection term and singular potentials on one extremity of the interval. A Dirichlet boundary condition depending on the time-variable is imposed. Using nonlinear capacity estimates, we establish sufficient conditions for the nonexistence of weak solutions to the considered problem. In particular, when the boundary condition is independent of time, we show the existence of a Fujita-type critical exponent.

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“…Again, by (59), we obtain (57), which implies that ζ 1 < 0 and ζ 2 < 0. Thus, by (10), for all θ > 0, there holds…”

Section: Discussionmentioning

confidence: 95%

“…Using the concavity approach, the blow-up of solutions was investigated. We also refer to [9][10][11][12][13][14][15], where the large-time behavior of solutions to nonlinear wave equations has been studied by the energy and concavity methods. The applications of fractional calculus are broad.…”

Section: Introductionmentioning

confidence: 99%