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- W2038158216 abstract "This work is concerned with the inverse problem of determining initial value of the Cauchy problem for a nonlinear diffusion process with an additional condition on free boundary. Considering the flow of water through a homogeneous isotropic rigid porous medium, we have such desire: for every given positive constants K and T0, to decide the initial value u0 such that the solution u(x, t) satisfies (mathop {sup }limits_{x in H_u (T_0 )} |x| geqslant K), where Hu(T0) = {x, ℝN: u(x, T0) > 0}. In this paper, we first establish a priori estimate ut ⩾ C(t)u and a more precise Poincare type inequality (left| phi right|_{L^2 (B_varrho )}^2 leqslant varrho left| {nabla phi } right|_{L^2 (B_varrho )}^2 ), and then, we give a positive constant C0 and assert the main results are true if only (left| {u_0 } right|_{L^2 (mathbb{R}^N )} geqslant C_0 )." @default.
- W2038158216 created "2016-06-24" @default.
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- W2038158216 date "2013-12-01" @default.
- W2038158216 modified "2023-09-28" @default.
- W2038158216 title "On an over-determined problem of free boundary of a degenerate parabolic equation" @default.
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- W2038158216 doi "https://doi.org/10.1007/s10492-013-0033-3" @default.
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