Solvability, continuous dependence and asymptotic expansion of solutions in a small parameter of Dirichlet problem for a nonlinear Kirchhoff wave equation
نویسندگان
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 University of Khanh Hoa, 01 Nguyen Chanh Str., Nha Trang City, Vietnam
3 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
4 Vietnam National University, Ho Chi Minh City, Vietnam
doi
10.22075/ijnaa.2023.30205.4362چکیده
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.
