Giải pháp toàn phần trong phương trình phản ứng-mạng di chuyển khuếch tán với phi tuyến hai ổn định trong môi trường không đồng nhất

Science China Mathematics - Tập 53 - Trang 1775-1786 - 2010
NaiWei Liu1,2, WanTong Li2
1School of Mathematics and Informational Science, Yantai University, Yantai, China
2School of Mathematics and Statistics, Lanzhou University, Lanzhou, China

Tóm tắt

Bài báo này bàn về các giải pháp toàn phần (t ∈ ℝ) cho các phương trình phản ứng-mạng di chuyển khuếch tán trong môi trường không đồng nhất. Bằng cách sử dụng các biên cong di chuyển nối giữa một trạng thái tĩnh không ổn định hằng số và một trạng thái tĩnh ổn định, chúng tôi đã chứng minh rằng tồn tại các giải pháp toàn phần hành xử như hai biên cong di chuyển từ hai hướng đối lập và tiếp cận nhau. Hơn nữa, chúng tôi chứng minh rằng giải pháp toàn phần như vậy là duy nhất và ổn định Liapunov. Kỹ thuật chính là mô tả hành vi tiệm cận của các giải pháp ở vô cùng theo các giải pháp phụ thích hợp và các giải pháp trên.

Từ khóa

#giải pháp toàn phần #phương trình phản ứng-mạng di chuyển khuếch tán #phi tuyến hai ổn định #môi trường không đồng nhất #ổn định Liapunov

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