Nonexistence of Global Solutions for the Kirchhoff-Type Equation with Fractional Damped

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...

Finite time blow up of solutions of the Kirchhoff-type equation with variable exponents

In this work, we investigate the following Kirchhoff-type equation with variable exponent nonlinearities u_{tt}-M(‖∇u‖²)△u+|u_{t}|^{p(x)-2}u_{t}=|u|^{q(x)-2}u. We proved the blow up of solutions in finite time by using modified energy functional method.

Nonexistence of global solutions for a fractional problems with a nonlinearity of the Fisher type

This paper deals with the Cauchy problem for a nonlinear hyperbolic equation D1+α 0|t u+D 0|tu+ (− ) γ 2 u = h(t, x) | u |p| 1 − u |q, posed in Q = R+ × R, where pi, qi > 1, −1 < α < 1, 0 < β < 2, 0 < γ ≤ 2, and β < 1+α with given initial position and velocity u(x, 0) = u0(x), ut (x, 0) = u1(x), and the Cauchy problem for a nonlinear hyperbolic system with initial data   D 1+α1 0|t...

Analytical solutions for the fractional Fisher's equation

In this paper, we consider the inhomogeneous time-fractional nonlinear Fisher equation with three known boundary conditions. We first apply a modified Homotopy perturbation method for translating the proposed problem to a set of linear problems. Then we use the separation variables  method to solve obtained problems. In examples, we illustrate that by right choice of source term in the modified...

Global Nonexistence in a Nonlinearly Damped Wave Equation