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Về một nghiệm yếu tương ứng với phương trình parabolic suy yếu gấp đôi
Tóm tắt
Sự tồn tại của nghiệm yếu cho phương trình Laplace $p(x)$-Laplacian gấp đôi được nghiên cứu. Giả sử rằng $b(x,t)| _{(x,t)\in \varOmega \times [0,T]}>0$ nhưng $b(x,t) | _{(x,t)\in \partial \varOmega \times [0,T]}=0$, $A'(s)=a(s)\geq 0$ và $A(s)$ là một hàm tăng liên tục nghiêm ngặt với $A(0)=0$. Một nghiệm yếu tương ứng với phương trình parabolic suy yếu gấp đôi được giới thiệu. Sự tồn tại của nghiệm yếu được chứng minh thông qua phương pháp điều hòa parabolic. Định lý ổn định của nghiệm yếu được thiết lập độc lập với điều kiện biên. Đặc biệt, điều kiện giá trị khởi đầu được thỏa mãn trong một dạng tổng quát hơn.
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#nghiệm yếu #phương trình parabolic #tồn tại #ổn định #điều kiện giá trị khởi đầuTài liệu tham khảo
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