This paper is devoted to explore tilted kinematic self-similar solutions of the the general cylindrical symmetric spacetimes. These solutions are of the first, zeroth, second and infinite kinds for the perfect fluid and dust cases. Three different equations of state are used to obtain these solutions. We obtain a total of five independent solutions. The correspondence of these solutions with th...

The existence of self-similar solutions with a finite first moment is established for the Oort-Hulst-Safronov coagulation equation when the coagulation kernel is given by a(y, y∗) = yλ + yλ ∗ for some λ ∈ (0, 1). The corresponding self-similar profiles are compactly supported and have a discontinuity at the edge of their support. MSC 2000: 45K05, 45M05, 82C21

Numerical approximations of shock waves sometimes suffer from instabilities called carbuncles. Techniques for suppressing carbuncles are trialand-error and lack in reliability and generality, partly because theoretical knowledge about carbuncles is equally unsatisfactory. It is not known which numerical schemes are affected in which circumstances, what causes carbuncles to appear and whether ca...

In this paper we study self-similar solutions for nonlinear Schrödinger equations using a scaling technique and the partly contractive mapping method. We establish the small global well-posedness of the Cauchy problem for nonlinear Schrödinger equations in some non-reflexive Banach spaces which contain many homogeneous functions. This we do by establishing some a priori nonlinear estimates in B...

We present numerical solutions of a two-dimensional Riemann problem for the unsteady transonic small disturbance equations that provides an asymptotic description of the Mach reflection of weak shock waves. We develop a new numerical scheme to solve the equations in selfsimilar coordinates and use local grid refinement to resolve the solution in the reflection region. The solutions contain a re...