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Blow-up phenomena for a nonlocal quasilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux

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  • This paper deals with blow-up phenomena for an initial boundary value problem of a nonlocal quasilinear parabolic equation with time-dependent coefficients in a bounded star-shaped region under nonlinear boundary flux. Using the auxiliary function method and modified differential inequality technique, we establish some conditions on time-dependent coefficients and nonlinearities to guarantee that the solution $u(x,t)$ exists globally or blows up at some finite time $t^{\ast}$. Moreover, upper and lower bounds of $t^{\ast}$ are obtained under suitable measure in high-dimensional spaces. Finally, some application examples are presented.
    Mathematics Subject Classification: Primary: 35K59, 35B44; Secondary: 35B40.

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