Arbitrary initial energy blow up for fourth-order viscous damped wave equation with exponential-type growth nonlinearity

Existence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation

‎In this paper‎, ‎we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation‎. ‎Moreover‎, ‎the finite-time blow-up of the solution for the equation is investigated by the concavity method‎.

Finite time blow-up results for the damped wave equations with arbitrary initial energy in an inhomogeneous medium

In this paper we consider the long time behavior of solutions of the initial value problem for the damped wave equation of the form utt − ρ(x) ∆u+ ut +m u = f(u) with some ρ(x) and f(u) on the whole space R (n ≥ 3). For the low initial energy case, which is the non-positive initial energy, based on concavity argument we prove the blow up result. As for the high initial energy case, we give out ...

Damped Wave Equation with a Critical Nonlinearity

We study large time asymptotics of small solutions to the Cauchy problem for nonlinear damped wave equations with a critical nonlinearity { ∂2 t u+ ∂tu−∆u+ λu 2 n = 0, x ∈ Rn, t > 0, u(0, x) = εu0 (x) , ∂tu(0, x) = εu1 (x) , x ∈ Rn, where ε > 0, and space dimensions n = 1, 2, 3. Assume that the initial data u0 ∈ H ∩H, u1 ∈ Hδ−1,0 ∩H−1,δ, where δ > n 2 , weighted Sobolev spaces are H = { φ ∈ L; ...

Blow Up in a Nonlinearly Damped Wave Equation

In this paper we consider the nonlinearly damped semilinear wave equation utt −∆u + aut |ut|m−2 = bu|u|p−2 associated with initial and Dirichlet boundary conditions. We prove that any strong solution, with negative initial energy, blows up in finite time if p > m. This result improves an earlier one in [2].

Blow-Up in a Fourth-Order Semilinear Parabolic Equation From . . .