Gradient estimates for degenerate diffusion equations. I
Copyright policy )Gradient estimates for degenerate diffusion equations. I
SynopsisWe establish upper and lower bounds for various norms of solutions and their gradients for the equation ut = div (|∇u|m−1 ∇u) in ℝN in terms of the norms of the initial data. Based on the L∞ estimate of ∇u, we conclude that u(x, t) is Lipschitz continuous in space-time, for all t>0, whenever u(x,0) is in L1(ℝN).
- Purdue University System United States
- DigiZeitschriften Germany
- Purdue University West Lafayette United States
decay estimates, convexity, Flows in porous media; filtration; seepage, Asymptotic behavior of solutions to PDEs, Smoothness and regularity of solutions to PDEs, porous medium, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, gradient estimates, Lipschitz continuity, Degenerate parabolic equations, A priori estimates in context of PDEs, Article, Lipschitz continuity of the solution, 510.mathematics, regularity properties, Initial-boundary value problems for second-order parabolic equations, degenerate parabolic problem, Nonlinear parabolic equations, degenerate diffusion equations, Initial value problems for second-order parabolic equations, gradients of solutions
decay estimates, convexity, Flows in porous media; filtration; seepage, Asymptotic behavior of solutions to PDEs, Smoothness and regularity of solutions to PDEs, porous medium, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, gradient estimates, Lipschitz continuity, Degenerate parabolic equations, A priori estimates in context of PDEs, Article, Lipschitz continuity of the solution, 510.mathematics, regularity properties, Initial-boundary value problems for second-order parabolic equations, degenerate parabolic problem, Nonlinear parabolic equations, degenerate diffusion equations, Initial value problems for second-order parabolic equations, gradients of solutions
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