论文标题
一层弱耦合的二阶抛物线系统的解决方案的尖锐估计值
Sharp pointwise estimates for solutions of weakly coupled second order parabolic system in a layer
论文作者
论文摘要
我们处理$ M $ -COMPONENT VALE-VALUED解决方案，以解决cauchy问题的线性和非均匀性弱耦合的二阶抛物线系统中的线性$ {\ MathBb r}^{n+1} _t = {我们假设该系统的系数是真实的，仅取决于$ t $，$ n \ geq 1 $和$ t <\ iffty $。同质系统在$ [l^p（{\ Mathbb r}^n）]^m $中的初始数据考虑考虑，$ 1 \ leq p \ leq \ leq \ infty $。对于非均匀系统，我们假设初始函数等于零，右侧属于$ [l^p（{\ Mathbb r}^{n+1} _t）]^m \ cap [c^α\ big big（\ big） 1）$。在这些问题的解决方案及其方向导数方面的尖锐系数估计中，明确的公式得到了。
We deal with $m$-component vector-valued solutions to the Cauchy problem for linear both homogeneous and nonhomogeneous weakly coupled second order parabolic system in the layer ${\mathbb R}^{n+1}_T={\mathbb R}^n\times (0, T)$. We assume that coefficients of the system are real and depending only on $t$, $n\geq 1$ and $T<\infty$. The homogeneous system is considered with initial data in $[L^p({\mathbb R}^n)]^m$, $1\leq p \leq \infty $. For the nonhomogeneous system we suppose that the initial function is equal to zero and the right-hand side belongs to $[L^p({\mathbb R}^{n+1}_T)]^m\cap [C^α\big (\overline{{\mathbb R}^{n+1}_T} \big )]^m $, $α\in (0, 1)$. Explicit formulas for the sharp coefficients in pointwise estimates for solutions of these problems and their directional derivative are obtained.
