The interface blow-up phenomenon and local estimates for doubly degenerate parabolic equations
The interface blow-up phenomenon and local estimates for doubly degenerate parabolic equations
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DOI：
10.1080/00036810701435711
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发表时间：
2007-01-01
影响因子：
1.1
通讯作者：
Tedeev, A. F.
中科院分区：
文献类型：
--
作者：
Tedeev, A. F.
本文研究了两类退化抛物型方程的偏导数u/偏导数t = div（a{竖线x竖线u（m-1）竖线Du竖线（lambda-1）Du）和rho（竖线x竖线）偏导数u/偏导数t = div（u（m-1）竖线Du竖线（lambda-1）Du），其中lambda > 0，m + lambda-2> 0，a（s）和rho（s）是正连续函数（0，无穷大）。我们研究在哪些条件下a（s）和rho（s）的行为，相应的Cauchy问题的非负解具有有限的传播速度或界面吹尖速度。此外，我们还研究了相应的柯西问题的解的局部性态下的初始数据的最优假设。
We study two classes of degenerate parabolic equations of the formspartial derivative u/partial derivative t = div(a{vertical bar x vertical bar u(m-1) vertical bar Du vertical bar(lambda-1) Du) and rho(vertical bar x vertical bar) partial derivative u/partial derivative t = div(u(m-1) vertical bar Du vertical bar(lambda-1) Du),where lambda > 0, m + lambda -2 > 0 and a(s) and rho(s) are positive continuous functions oil (0,infinity).We examine under which conditions oil behaviour of a(s) and rho(s), corresponding rion-negative solutions of the Cauchy problems possess the Finite speed of propagatious or the interface blow-tip pheriorneria. Moreover, we study local behaviour of solutions of the corresponding Cauchy problems under the optimal assumptions of initial data.