GLOBAL EXISTENCE AND NONEXISTENCE OF SOLUTIONS FOR SEMILINEAR WAVE EQUATION WITH A NEW CONDITION
Sabitbek B.
2023American Institute of Mathematical Sciences
Discrete and Continuous Dynamical Systems- Series A
2023#43Issue 72637 - 2657 pp.
In this paper, we consider the initial-boundary problem for semilinear wave equation with a new condition on the source term f(u) such as (Formula Presented) for some positive constants α, β, and σ, where α > 2 and β < λ1(α−2) with λ1 being a first eigenvalue of Dirichlet-Laplacian. The condition on f(u) with 2 β = 0 and σ = 0 was studied in [13] and [3]. By introducing a family of potential wells, we are able to establish the invariant sets, vacuum isolation of solutions, and a threshold result of global existence and nonexistence of solutions with the new condition on a source term. Moreover, we discuss the global existence and nonexistence of solutions for problem with initial condition E(0) < d and critical initial condition E(0) = d.
blow-up solution , global existence , potential wells theory , Semilinear wave equation
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Queen Mary University of London, United Kingdom
Institute of Mathematics and Mathematical Modeling, Kazakhstan
Queen Mary University of London
Institute of Mathematics and Mathematical Modeling
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026