Propagation of perturbation in a singular Cauchy problem for degenerate quasilinear parabolic equations
Propagation of perturbation in a singular Cauchy problem for degenerate quasilinear parabolic equations
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DOI：
10.1070/sm1996v187n09abeh000161
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
A E Shishkov
中科院分区：
文献类型：
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作者：
A E Shishkov
研究了一类发散的任意阶拟线性抛物型方程的柯西问题。这一类特别包含非定常牛顿和非牛顿过滤的方程。从可解性理论的观点出发，证明了对于具有最低局部正则性的任意初始函数，广义解的支集的演化速率是有限的。得到了这一比率的上界估计，它对大的和小的时间都是精确的。
Cauchy problems for a wide class of 'doubly degenerate' divergent quasilinear parabolic equations of an arbitrary order are studied. This class contains, in particular, the equations of non-stationary Newtonian and non-Newtonian filtration. For arbitrary initial functions of the lowest local regularity acceptable from the viewpoint of the theory of solubility it is proved that the rate of evolution of the supports of the generalized solutions is finite. Upper estimates of this rate are obtained which are exact both for large and small times.