We develop the perturbation theory for propagators, with the objective to prove Gaussian bounds. Let U be a strongly continuous propagator, i.e., a family of operators describing the solutions of a non-autonomous evolution equation, on an Lp-space, and assume that U is positive and satisfies Gaussian upper and lower bounds. Let V be a (time-dependent) potential satisfying certain Miyadera condi...

This paper is concerned with the interactions of δ-shock waves for the Aw-Rascle traffic model with split delta functions. The solutions are obtained constructively when the initial data are three piecewise constant states. The global structure and large time-asymptotic behaviors of the solutions are analyzed case by case. Moreover, it can be found that the Riemann solutions are stable for such...

In this article we decide to define a modified homotopy perturbation for solving non-linear integral equations. Almost, all of the papers that was presented to solve non-linear problems by the homotopy method, they used from two non-linear and linear operators. But we convert a non-linear problem to two suitable non-linear operators also we use from appropriate bases functions such as Legendre ...

This study is about Complexes of Li doped silicon carbide nanotube with Thymine and Cytosine ingas phase and aqueous solutions. Li doped silicon carbide nanotube and its pyrimidine nucleobasecompounds were first modeled by Quantum mechanical calculations in gas phase and in water.Calculated binding energies indicated the stronger ability of thymine to functionalize silicon carbidenanotube than ...

Here Ω is the unit disk centered at the origin, containing a small hole of radius ε centered at x = 0, i.e. Ωε = {x | |x| ≤ ε}. Calculate the exact solution, and from it determine an approximation to the solution in the outer region |x| ≫ O(ε). Can you re-derive this result from singular perturbation theory in the limit ε → 0? (Hint: the leading-order outer problem for Case I is different from ...

The quarks of quark models cannot be identified with the quarks of the QCD Lagrangian. We review the restrictions that gauge field theories place on any description of physical (colour) charges. A method to construct charged particles is presented. The solutions are applied to a variety of applications. Their Green’s functions are shown to be free of infra-red divergences to all orders in pertu...

This work concerns how to find the double periodic form of approximate solutions of the perturbed combined KdV (CKdV) equation with variable coefficients by using the homotopic mapping method. The obtained solutions may degenerate into the approximate solutions of hyperbolic function form and the approximate solutions of trigonometric function form in the limit cases. Moreover, the first order ...

These two lectures cover some of the advances that underpin recent progress in deriving continuum solutions from the exact renormalization group. We concentrate on concepts and on exact non-perturbative statements, but in the process will describe how real non-perturbative calculations can be done, particularly within derivative expansion approximations. An effort has been made to keep the lect...

We construct the non uniform AdS black string solution with a perturbation theory in six dimensions, focusing on the backreacting second order correction. The backreactions at second order give the first relevant corrections to the thermodynamical quantities. Our results show that for configurations with horizon radius and length in the extradimension small compared to the AdS radius, the prope...

We consider the dynamics of a multi-component scalar field on super-horizon scales in the context of inflationary cosmology. We present a method to solve the perturbation equations on super-horizon scales, i.e., in the long wavelength limit, by using only the knowledge of spatially homogeneous background solutions. In doing so, we clarify the relation between the perturbation equations in the l...