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- W1989311788 abstract "We derive estimates of solutions of the semilinear 2mth-order parabolic equation of diffusion–absorption typeut=−(−Δ)mu−|u|p−1uinRN×R+,m⩾2,p>1, with bounded initial data u0 from Lq or other functional spaces. For m=1, i.e., for the semilinear heat equation with absorption intensively studied from the 1970s, basic global L∞-estimates are straightforward and guaranteed by the Maximum Principle. We show that for m⩾2, where comparison or order-preserving properties of parabolic flows fail, some similar estimates can be obtained by scaling techniques establishing the rates of decay of the solutions as t→∞ and the behaviour as t→0." @default.
- W1989311788 created "2016-06-24" @default.
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- W1989311788 date "2008-05-01" @default.
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- W1989311788 title "<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msup><mml:mi>L</mml:mi><mml:mo>∞</mml:mo></mml:msup></mml:math> and decay estimates for higher-order semilinear diffusion–absorption equations" @default.
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- W1989311788 doi "https://doi.org/10.1016/j.jmaa.2007.05.082" @default.
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