Abstract
This paper deals with blow-up phenomena for an initial boundary value problem of a porous medium equation with time-dependent coefficients and inner absorption term 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 coefficient and nonlinear functions to guarantee that the solution $u(x,t)$ exists globally or blows up at some finite time $t^{\ast}$. Moreover, the upper and lower bounds for $t^{\ast}$ are derived in the higher dimensional space. Finally, some examples are presented to illustrate applications of our results.
Citation
Suping Xiao. Zhong Bo Fang. "Blow-up Phenomena for a Porous Medium Equation with Time-dependent Coefficients and Inner Absorption Term Under Nonlinear Boundary Flux." Taiwanese J. Math. 22 (2) 349 - 369, April, 2018. https://doi.org/10.11650/tjm/170802
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