EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR A STRONGLY DAMPED WAVE EQUATION WITH POLYNOMIAL NONLINEARITIES

• Tác giả: Dang Thanh Son, Xuan Dong Le, Duong Toan Nguyen, Duy Tan Nguyen
• Ngôn ngữ: eng
• Thông tin xuất bản: Haiphong University Journal of Science, 2024
• Mô tả vật lý: tr.63
• Bộ sưu tập: Metadata
• ID: 245277

Tóm tắt

This paper studies the first initial boundary value problem for the strongly damped wave equations on a bounded domain   3 . Under the polynomial growth rate of the nonlinearity f and an external force g independent on time t, we prove the existence and uniqueness of a weak solution. Finally, we show the existence of a weak global attractor for the continuous semigroup generated by the weak solution.