loading page

Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term
  • +1
  • Nguyen Thanh Long,
  • Nguyen Huu Nhan,
  • Le Thi Phuong Ngoc,
  • Doan Thi Nhu Quynh
Nguyen Thanh Long
University of Natural Science, Vietnam National University Ho Chi Minh City

Corresponding Author:[email protected]

Author Profile
Nguyen Huu Nhan
Nguyen Tat Thanh University
Author Profile
Le Thi Phuong Ngoc
University of Khanh Hoa
Author Profile
Doan Thi Nhu Quynh
University of Food Industry
Author Profile


This paper is devoted to the study of existence, uniqueness, continuous dependence, general decay of solutions of an initial boundary value problem for a viscoelastic wave equation with strong damping and nonlinear memory term. At first, we state and prove a theorem involving local existence and uniqueness of a weak solution. Next, we establish a sufficient condition to get an estimate of the continuous dependence of the solution with respect to the kernel function and the nonlinear terms. Finally, under suitable conditions to obtain the global solution, we prove the general decay property with positive initial energy for this global solution.