An initial-value problem in shock stability

Positive solutions for discrete fractional initial value problem

‎‎In this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎The solutions of fractional difference equation are the size of tumor in model tumor growth described by the Gompertz f...

Initial-value-problem solution for isolated rippled shock fronts in arbitrary fluid media.

Following the work of Roberts [Los Alamos Scientific Laboratory Report No. LA-299, 1945 (unpublished)], we investigate the effect of small two-dimensional perturbations on an isolated, planar shock front moving steadily through an inviscid fluid medium with an arbitrary equation of state (EOS). In the context of an initial-value problem, we derive explicit analytical expressions for the lineari...

The initial value problem in numerical relativity

The conformal method for constructing initial data for Einstein’s equations is presented in both the Hamiltonian and Lagrangian picture (extrinsic curvature decomposition and conformal thin sandwich formalism, respectively), and advantages due to the recent introduction of a weight-function in the extrinsic curvature decomposition are discussed. I then describe recent progress in numerical tech...

An Initial and Boundary Value Problem Modeling Fish-like Swimming

In this paper we consider an initial and boundary value problem modeling the self-propelled motion of solids in a bi-dimensional viscous incompressible uid. The self-propelling mechanism, consisting in appropriate deformations of the solids, is a simpli ed model for the propulsion mechanism of sh-like swimmers. The governing equations are composed of the Navier-Stokes equations for the uid, cou...

An initial - boundary - value problem for the Korteweg -