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Các thuộc tính giá trị trung bình tiệm cận cho các phương trình elliptic và parabolic có hai pha
Tóm tắt
Chúng tôi đặc trưng hóa một công thức giá trị trung bình tiệm cận theo nghĩa độ nhớt cho phương trình elliptic hai pha
$$\begin{aligned} -{\textrm{div}}(|\nabla u |^{p-2}\nabla u+ a(x)|\nabla u |^{q-2}\nabla u)=0 \end{aligned}$$
và phương trình parabol hai pha đã chuẩn hóa
$$\begin{aligned} u_t=|\nabla u |^{2-p}{\textrm{div}}(|\nabla u |^{p-2}\nabla u+ a(x,t)|\nabla u |^{q-2}\nabla u), \quad 1
Từ khóa
#phương trình elliptic #phương trình parabolic #giá trị trung bình tiệm cận #độ nhớt #phương trình p-Laplace #phương trình p(x)-LaplaceTài liệu tham khảo
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