In this work, we deal with the wave equation variable coefficients. Under proper conditions on coefficients, prove nonexistence of global solutions.

In the paper, problems of controllability and approximate are studied for heat equation w t = 1/ρ ( kw x ) + γ , > 0, ∈ (0, T ), controlled by Dirichlet boundary condition. Control is considered in L ∞ ). It proved that each initial state this system approximately controllable to any its end a given time 0.

An N-dimensional nonlinear Fokker-Planck equation is investigated here by considering the time dependence of the coefficients, where drift-controlled and source terms are present. We exhibit the exact solution based on the generalized Gaussian function related to the Tsallis statistics. Furthermore, we show that a rich class of diffusive processes, including normal and anomalous ones, can be ob...

The exact traveling wave solutions of the nonlinear variable coefficients Burgers-Fisher equation and the generalized Gardner equation with forced terms can be found in this article using the generalized ( ′ G )-expansion method. As a result, hyperbolic, trigonometric and rational function solutions with parameters are obtained. When these parameters are taken special values, the solitary wave ...