Blow-up of Result in a Nonlinear Wave Equation with Delay and Source Term - (x, In this paper we consider the initial boundary value problem for a nonlinear damping and a delay term of the form: |u_t|^lu_tt- u; u_tt+_1|u_t|^m-2u_t\\+_2|u_t(t-)|^m-2u_t(t-)=b|u|^p-2u, t) -; on, with initial conditions and Dirichlet boundary conditions. Under appropriate conditions; ., we prove that there are solutions with negative initial energy that blow-up finite time if (Discontinuity, Nonlinearity, and Complexity, 2026)
In this paper we consider the initial boundary value problem for a nonlinear damping and a delay term of the form: $$ |u_t|^{l}u_{tt}-\Delta u (x,t) -\Delta u_{tt}+\mu_1|u_t|^{m-2}u_t\\+\mu_2|u_t(t-\tau)|^{m-2}u_t(t-\tau)=b|u|^{p-2}u, $$ with initial conditions and Dirichlet boundary conditions. Under appropriate conditions on $\mu_1$, $\mu_2$, we prove that there are solutions with negative initial energy that blow-up finite time if $p \geq \max\{l+2,m\}$.