EXISTENCE AND UNIQUENESS OF WEAK SOLUTIONS FOR A SEMILINEAR HEAT EQUATION WITH MEMORY

• Ngôn ngữ: eng
• Thông tin xuất bản: Tạp chí Khoa học - Trường Đại học Hải Phòng: Kinh tế và Kỹ thuật - Công nghệ, 2020
• Mô tả vật lý: tr.108
• Bộ sưu tập: Báo, Tạp chí
• ID: 312330

Tóm tắt

The first problem posed when studying the classes of PDEs is well-posedness (as V.P.Maslov is impressed that a PDE of practical significance then it will definitely be solutions,some kind of solutions). The well-posedness of a problem refers to whether the problem hasa solution, a unique solution and continuous dependence on the initial data of solution. Inthis paper we prove the well-posedness of weak solutions to a semilinear heat equation withmemory and the nonlinearity f of exponential type by the Galerkin approximation andcompactness method. The main novelty of our result is that no restriction on the growth ofthe nonlinearities is imposed.