L∞ and decay estimates for higher-order semilinear diffusion–absorption equations
L∞ and decay estimates for higher-order semilinear diffusion–absorption equations
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高阶半线性扩散吸收方程的 L∞ 和衰减估计
DOI：
10.1016/j.jmaa.2007.05.082
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
T. Gollan
中科院分区：
文献类型：
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作者：
N. Turner;T. Gollan
在Lq或其它泛函空间中，得到了具有有界初值u 0的半线性2 m阶抛物型扩散-吸收方程解的估计.对于m=1，即，对于自20世纪70年代以来被广泛研究的半线性热方程，基本的整体L∞估计是直接的，并由极大值原理保证。我们证明了对于m ∈ 2，当抛物流的比较或保序性质失效时，通过标度技术建立解在t→∞时的衰减率和在t→0时的行为，可以得到一些类似的估计。
We derive estimates of solutions of the semilinear 2mth-order parabolic equation of diffusion–absorption type with bounded initial data u0from Lqor 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.