We demonstrate that partner symmetries provide a lift of noninvariant solutions of three-dimensional Boyer-Finley equation to noninvariant solutions of four-dimensional hyperbolic complex MongeAmpère equation. The lift is applied to noninvariant solutions of the Boyer-Finley equation, obtained earlier by the method of group foliation, to yield noninvariant solutions of the hyperbolic complex Mo...

We demonstrate that partner symmetries provide a lift of noninvariant solutions of three-dimensional Boyer-Finley equation to noninvariant solutions of four-dimensional hyperbolic complex MongeAmpère equation. The lift is applied to noninvariant solutions of the Boyer-Finley equation, obtained earlier by the method of group foliation, to yield noninvariant solutions of the hyperbolic complex Mo...

It is shown that the fundamental solution of a hyperbolic partial differential equation with time delay has a natural probabilistic structure, i.e. is approximately Gaussian, as t → ∞. The proof uses ideas from the DeMoivre proof of the Central Limit Theorem. It follows that solutions of the hyperbolic equation look approximately like solutions of a diffusion equation with constant convection a...

Abstract. We present a phenomenological theory for phase transition dynamics with memory which yields a hyperbolic generalization of the classical phase field model when the relaxation kernels are assumed to be exponential. Thereafter, we focus on the implications of our theory in the hyperbolic case, and we derive asymptotically an equation of motion in two dimensions for the interface between...

In this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. We prove a posteriori $ L^2(L^2)$ and error estimates for this method under minimal regularity hypothesis. Test problem of an application of the wave equation in the laser is presented to verify the efficiency and accuracy of the method.

In this paper we present a hyperbolic partial differential equation (PDE) in one space and one time dimension. This equation arose in a study of numerical schemes for simulating evolving river topographies. The solution of this PDE, whose initial data are specified along a characteristic, is very similar to that of the canonical diffusion equation. This interesting example provides insight into...