Scholarlink

Abstract <p>This paper investigates the existence and uniqueness of smooth solutions to the Cauchy problem for a class of nonlinear wave equations in 3D spaces. Under appropriate conditions on the nonlinearities such as concavity, monotonicity, and smoothness, an existence theorem is established, guaranteeing a smooth and bounded solution to the problem. Furthermore, uniform convergence of the corresponding successive approximations to the solution is demonstrated, with a convergence rate characterized by an exponentially decreasing geometric progression. A uniqueness theorem is also proven for solutions within a specified class of smooth and bounded functions. Specific examples of nonlinearities are presented to highlight the applicability and significance of the results obtained.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Solvability of the Cauchy Problem to Nonlinear Wave Equations in 3D Spaces

  • 期刊论文

  • 发表日期：

    2025年8月1日

查看全文
  • A. Kh. Khachatryan,
  • Kh. A. Khachatryan,
  • H. S. Petrosyan

摘要

Abstract

This paper investigates the existence and uniqueness of smooth solutions to the Cauchy problem for a class of nonlinear wave equations in 3D spaces. Under appropriate conditions on the nonlinearities such as concavity, monotonicity, and smoothness, an existence theorem is established, guaranteeing a smooth and bounded solution to the problem. Furthermore, uniform convergence of the corresponding successive approximations to the solution is demonstrated, with a convergence rate characterized by an exponentially decreasing geometric progression. A uniqueness theorem is also proven for solutions within a specified class of smooth and bounded functions. Specific examples of nonlinearities are presented to highlight the applicability and significance of the results obtained.