In this paper we consider a class of quasilinear, non-strictly hyper-bolic 2 2 systems in two space dimensions. Our main result is nite speed of propagation of the support of smooth solutions for these systems. As a consequence, we establish non-existence of global smooth solutions for a class of suuciently large, smooth initial data. The non-existence result applies to systems in conservation ...

We prove existence and uniqueness results for the time-dependent Hartree approximation arising in quantum dynamics. The equations of motion form a coupled system nonlinear Schr{\"o}dinger evolution product state approximations. They are prominent example dimension reduction context Dirac-Frenkel variational principle. handle case Coulomb potentials thanks to Strichartz estimates. Our main resul...

this paper presents a class of theoretical and iterative method for linear partial differential equations. an algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. in this technique, the solution is calculated in the form of a series with easily computable components. there test modeling problems from mathematical mechanic, physi...

We extend all previous results of our [Sm4], [Sm5] to the case of general (non-diagonal coefficents) Quasilinear First Order Hyperbolic Systems, in slab domains with an odd number of Spacial Dimensions greater than three, prove a comparision Principle for viscosity sub and super solutions of such general systems, and apply our results to the Cauchy Problem for the Einstein Field Equations. We s...

I prove that the initial-value problem for the motion of a certain type of elastic body has a solution for all time if the initial data are sufficiently small. The body must fill all of three-space, obey a "neo-Hookean" stress-strain law, and be incompressible. The proof takes advantage of the delayed singularity formation which occurs for solutions of quasilinear hyperbolic equations in more t...

About twenty years ago, V. P. Maslov [1] put forward the idea that numerous quasilinear hyperbolic systems have only finite number of singular solution in general position. These solutions are shock waves, “infinitely narrow” solitons and point singularities of the type of the square root of a quadratic form. He has also stated conjecture that such solutions for shallow water equation can descr...

Hyperbolic systems of conservation laws augumented with an entropy inequality are studied. It is shown that such systems can be written in a (quasilinear) skewselfndjoint form. Centered differencing of such a form under the smooth regime ends up with a systematic recipe for constructing quasiconservative schemes where the global entropy conservation is recovered. Employing the above formulation...

Abstract. A generalized Cauchy problem for quasilinear hyperbolic functional differential systems is considered. A theorem on the local existence of weak solutions is proved. The initial problem is transformed into a system of functional integral equations for an unknown function and for their partial derivatives with respect to spatial variables. The existence of solutions for this system is p...