Theory of impulsive partial differential equations can be applied to many fields, such as to biology, population growth, engineering, generic repression, control theory and climate model. In the last few years, the fundamental theory of partial differential equations with impulses has undergone intensive development. The qualitative theory of this class of equations, however, is still in an ini...

We consider the Schrödinger equation with no radial assumption on real hyperbolic spaces. We obtain sharp dispersive and Strichartz estimates for a large family of admissible pairs. As a first consequence, we obtain strong wellposedness results for NLS. Specifically, for small intial data, we prove L 2 and H 1 global wellposedness for any subcritical nonlinearity (in contrast with the flat case...

  Diffusivity equation commonly used for pressure distribution prediction in porous media results from substituting equation of state and continuity equation in Navier-Stokes momentum equation. From mathematical point of view this equation format shows infinite propagation speed for pressure pulse through porous media, which is physically impossible. This issue may caused by numerous assumption...

It is proved that the Dirichlet problem is correct in the characteristic rectangle Dab = [0, a] × [0, b] for the linear hyperbolic equation ∂4u ∂x2∂y2 = p0(x, y)u + p1(x, y) ∂u ∂x + p2(x, y) ∂u ∂y + +p3(x, y) ∂2u ∂x∂y + q(x, y) with the summable in Dab coefficients p0, p1, p2, p3 and q if and only if the corresponding homogeneous problem has only the trivial solution. The effective and optimal ...

We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. by consideration of domain boundaries in two-dimensional critical systems, and the invariance of the hyperbolic length, we motivate a reformulation of the basic equation of conformal covariance. The scale factors gain a new, physical interpretation. We exhibit a fully ...

In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential hyperbolic differential equation in 3-dimensional. We show that Dirichlet-Neumann operators have same properties equations as elliptic equations. numerically implement coefficients of formulas. Moreover, Lipschitz type stability is established near edge domain by estimation...