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- W4387601163 abstract "We consider a generalized anisotropic curvature flow involving a positive power $ alpha $ of the curvature: $ V = A({bf n})H^{alpha} $ in a band domain $ Omega: = [-1,1]times mathbb{R}, $ where $ A $ is a smooth positive function, $ V, {bf n} $ and $ H $ denote the normal velocity, the unit normal vector and the curvature of a simple plane curve $ gamma_{t} $, respectively. In addition, we assume that $ gamma_{t} $ contacts $ partial_{pm}Omega $ with slopes equaling to $ pm k(t) $ for some bounded function $ k $. We first give the a priori $ C^2 $ estimates (including the uniform bound of $ H $, which plays a key role in the parabolicity of the equation) and show the time-global existence for the initial-boundary value problem. Then we construct an entire solution of the problem by renormalization method, and show that the entire solution propagates from $ -infty $ to $ +infty $, connecting two traveling waves at $ t = -infty $ and $ t = +infty $ in case $ k(t) $ tends to two positive constants as $ trightarrow mpinfty $." @default.
- W4387601163 created "2023-10-14" @default.
- W4387601163 creator A5018882355 @default.
- W4387601163 date "2023-01-01" @default.
- W4387601163 modified "2023-10-14" @default.
- W4387601163 title "Entire solutions of a generalized curvature flow connecting two traveling waves" @default.
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- W4387601163 doi "https://doi.org/10.3934/dcdsb.2023162" @default.
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