<p style='text-indent:20px;'>We consider a damped Klein-Gordon equation with variable diffusion coefficient. This problem is challenging because of the equation's unbounded nonlinearity. First, we study nonlinearity's continuity properties. Then existence and uniqueness solutions established. The main result solution map on set admissible parameters. Its application to parameter identific...

We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Gordon and Schrödinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on the value of the conserved Hamiltonian, below which the exponential potential energy is dominated by the kinetic energy via a Trudinger-Moser type inequality. We...

We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Gordon and Schrödinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on the value of the conserved Hamiltonian, below which the exponential potential energy is dominated by the kinetic energy via a Trudinger-Moser type inequality. We...