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Tính ổn định của phương trình Kawahara sửa đổi ngẫu nhiên
Tóm tắt
Trong bài báo này, chúng tôi xem xét bài toán Cauchy cho phương trình Kawahara sửa đổi ngẫu nhiên, một phương trình sóng nước nông bậc năm. Chúng tôi chứng minh tính ổn định cục bộ cho dữ liệu trong $H^{s}(\mathbb{R})$, với $s\geq -1/4$. Hơn nữa, chúng tôi đạt được sự tồn tại toàn cục cho các nghiệm trong không gian $L^{2}( \mathbb{R})$. Do sự không đối xứng không bằng 0 của hàm pha, một lập luận điểm cố định và phương pháp hạn chế Fourier được đề xuất.
Từ khóa
#phương trình Kawahara #phương trình sóng nước nông #bài toán Cauchy #tính ổn định #nghiệm toàn cục #hàm pha #phương pháp hạn chế FourierTài liệu tham khảo
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