Nonexistence of Global Solutions for the Strongly Damped Wave Equation with Variable Coefficients

Global Nonexistence in a Nonlinearly Damped Wave Equation

Global Existence of Ε−regular Solutions for the Strongly Damped Wave Equation

In this paper, we deal with the semilinear wave equation with strong damping. By choosing a suitable state space, we characterize the interpolation and extrapolation spaces of the operator matrix Aθ, analysis the criticality of the ε-regular nonlinearity with critical growth. Finally, we investigate the global existence of the ε-regular solutions which have bounded X ×X norms on their existence...

Global Nonexistence of the Solutions for a Nonlinear Wave Equation with the Q-laplacian

We study the global nonexistence of the solutions of the nonlinear qLaplacian wave equation utt −∆qu + (−∆)ut = |u|p−2u, where 0 < α ≤ 1, 2 ≤ q < p. We obtain that the solution blows up in finite time if the initial energy is negative. Meanwhile, we also get the solution blows up in finite time with suitable positive initial energy under some conditions.

The modified KdV equation with variable coefficients: Exact uni/bi-variable travelling wave-like solutions

In this paper, the modified Korteweg-de Vries (mKdV) equation with variable coefficients (vc-mKdV equation) is investigated via two kinds of approaches and symbolic computation. On the one hand, we firstly reduce the vc-mKdV equation to a second-order nonlinear nonhomogeneous ODE using travelling wave-like similarity transformation. And then we obtain its many types of exact fractional solution...

Existence, global nonexistence, and asymptotic behavior of solutions for the Cauchy problem of a multidimensional generalized damped Boussinesq-type equation

where u (x, t) denotes the unknown function, f (s) is the given nonlinear function, u0 (x) and u1 (x) are the given initial value functions, k is a constant, the subscript t indicates the partial derivative with respect to t, n is the dimension of space variable x, and △ denotes the Laplace operator in R. The effects of small nonlinearity and dispersion are taken into consideration in the deriv...