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- W2138443329 abstract "We investigate the boundedness and large time behavior of solutions of the Cauchy-Dirichlet problem for the one-dimensional degenerate parabolic equation with gradient nonlinearity: $$ u_t = (|u-x|^{p-2} u-x)_x+|u_x|^q qquad text{in}quad (0, +infty)tiles(0, 1),qquad q > p > 2.$$ We prove that: either $u_x$ blows up in finite time, or $u$ is global and converges in $W^{1, infty}$norm to the unique steady state. This in particular eliminates the possibility of global solutions with unbounded gradient. For that purpose a Lyapunov functional is constructed by the approach of Zelenyak." @default.
- W2138443329 created "2016-06-24" @default.
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- W2138443329 date "2015-01-01" @default.
- W2138443329 modified "2023-09-30" @default.
- W2138443329 title "Boundedness of global solutions of a p-Laplacian evolution equation with a nonlinear gradient term" @default.
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- W2138443329 doi "https://doi.org/10.3233/asy-141263" @default.
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