Initial traces and solvability of Cauchy problem to a semilinear parabolic system

• Fujishima Yohei

  Department of Mathematical and Systems Engineering, Faculty of Engineering, Shizuoka University

• Ishige Kazuhiro

  Graduate School of Mathematical Sciences, The University of Tokyo

抄録

Let (𝑢, 𝑣) be a solution to a semilinear parabolic system (P)    \begin{cases}𝜕_𝑡 𝑢 = 𝐷₁ Δ 𝑢+𝑣^𝑝 in 𝐑^𝑁 ×(0, 𝑇),   𝜕_𝑡 𝑣 = 𝐷₂ Δ 𝑣+𝑢^𝑞 in 𝐑^𝑁 ×(0, 𝑇),   𝑢, 𝑣 ≥ 0 in 𝐑^𝑁 ×(0, 𝑇),   (𝑢(⋅, 0), 𝑣(⋅, 0)) = (𝜇, 𝜈) in 𝐑^𝑁, \end{cases} where 𝑁 ≥ 1, 𝑇 > 0, 𝐷₁ > 0, 𝐷₂ > 0, 0 < 𝑝 ≤ 𝑞 with 𝑝𝑞 > 1 and (𝜇, 𝜈) is a pair of Radon measures or nonnegative measurable functions in 𝐑^𝑁. In this paper we study qualitative properties of the initial trace of the solution (𝑢, 𝑣) and obtain necessary conditions on the initial data (𝜇, 𝜈) for the existence of solutions to problem (P).

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

  Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ 73 (4), 1187-1219, 2021

  一般社団法人 日本数学会

キーワード

• semilinear parabolic system
• initial trace
• local existence
• nonexistence

詳細情報

• CRID: 1390289796573105792
• NII論文ID: 130008106923
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/84728472
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL書誌ID: 031756588
• Web Site: http://id.ndl.go.jp/bib/031756588
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I031756588
• 本文言語コード: en
• データソース種別:
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