Tính đối xứng trong PDE phi tuyến: Một số vấn đề còn bỏ ngỏ

Springer Science and Business Media LLC - Tập 15 - Trang 299-320 - 2014
Adriano Pisante1
1Department of Mathematics, University of Rome, La Sapienza, Roma, Italy

Tóm tắt

Trong ghi chú này, chúng tôi thảo luận về các tính chất đối xứng của các nghiệm cho các hệ phương trình vi phân riêng phần phi tuyến dạng vô hướng và vectơ. Các hệ phương trình quan tâm có tính chất biến thiên, ví dụ, chúng xuất hiện trong một số mô hình chuyển pha bậc nhất trong vật lý toán học (ví dụ, phân tách pha, siêu dẫn, tinh thể lỏng) và tự nhiên liên quan đến một số PDE trong hình học (bề mặt tối thiểu và ánh xạ điều hòa). Chúng tôi tổng hợp lại một số kết quả đã biết và trình bày một vài vấn đề mở về tính đối xứng của các hàm tối ưu cho tất cả các mô hình này.

Từ khóa

#tính đối xứng #phương trình vi phân riêng phần #mô hình chuyển pha #bề mặt tối thiểu #ánh xạ điều hòa

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