Nội dung được dịch bởi AI, chỉ mang tính chất tham khảo
Phát triển giao diện cho các phương trình phản ứng–khuếch tán suy thoái phi tuyến nhiều chiều
Tóm tắt
Bài báo này trình bày một phân loại đầy đủ về hành vi ngắn hạn của các bề mặt giao diện trong bài toán Cauchy cho phương trình vi phân phân cấp phi tuyến bậc hai suy thoái $$\begin{aligned} u_t-\Delta u^m +b u^\beta =0, \quad x\in {\mathbb {R}}^N, 01, C,\alpha , \beta >0, b \in {\mathbb {R}}$$. Bề mặt giao diện $$t=\eta (x)$$ có thể co lại, mở rộng hoặc giữ nguyên tùy thuộc vào sức mạnh tương đối của các thuật ngữ khuếch tán và phản ứng gần biên hỗ trợ, được biểu diễn bằng các tham số $$m,\beta , \alpha , sign\ b$$ và C. Trong tất cả các trường hợp, chúng tôi chứng minh công thức rõ ràng cho sự tiệm cận của giao diện và giải pháp cục bộ gần giao diện.
Từ khóa
#phương trình vi phân #phản ứng khuếch tán #hành vi giao diện #tiệm cận giao diệnTài liệu tham khảo
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