International Journal of Nonlinear Analysis and Applications

Solvability, continuous dependence and asymptotic expansion of solutions in a small parameter of Dirichlet problem for a nonlinear Kirchhoff wave equation

Document Type : Research Paper

Authors

1 Faculty of Applied Sciences, Ho Chi Minh City University of Food Industry, 140 Le Trong Tan Str., Tan Phu Dist., Ho Chi Minh City, Vietnam

2 Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, 227 Nguyen Van Cu Str., Dist. 5, Ho Chi Minh City, Vietnam

3 Vietnam National University, Ho Chi Minh City, Vietnam

4 University of Khanh Hoa, 01 Nguyen Chanh Str., Nha Trang City, Vietnam

Abstract

We study the existence, uniqueness, continuous dependence, and asymptotic expansion of solutions of the Dirichlet problem for a nonlinear Kirchhoff wave equation. At first, we state and prove a theorem involving the 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 nonlinear terms. Finally, an asymptotic expansion of high order in a small parameter of a weak solution is also discussed.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 9
September 2023
Pages 17-46
  • Receive Date: 15 March 2023
  • Accept Date: 21 June 2023