We establish the global existence of L∞ solutions for a model of polytropic gas flow with diffusive entropy. The result is obtained by showing the convergence of a class of finite difference schemes, which includes the Lax– Friedrichs and Godunov schemes. Such convergence is achieved by proving the estimates required for the application of the compensated compactness theory.

We study the Oseen problem with rotational e ect in the whole threedimensional space. Using a variational approach we prove existence and uniqueness theorems in anisotropically weighted Sobolev spaces. As the main tool we derive and apply an inequality of the Friedrichs-Poincaré type.

This paper presents a unified analysis of Discontinuous Galerkin methods to approximate Friedrichs' symmetric systems. An abstract set of conditions is identified at the continuous level to guarantee existence and uniqueness of the solution in a subspace of the graph of the differential operator. Then a general Discontinuous Galerkin method that weakly enforces boundary conditions and mildly pe...

We study the existence of global-in-time weak solutions to a coupled microscopicmacroscopic bead-spring model which arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier–Stokes equations in a bounded domain Ω ⊂ Rd, d = 2 or 3, for the velocity and the pressure of the fluid, with an ela...

By [Formula: see text] we denote the semigroup of operators generated by Friedrichs extension Schrödinger operator with inverse square potential defined in text]. In this paper, establish weighted text]-inequalities for maximal, variation, oscillation and jump associated text], where denotes Weyl fractional derivative. The range values that works is different when

This book is the third volume of a three-part textbook suitable for both graduate coursework and professional engineering research reference alike. Volume III focuses on time-dependent problems symmetric positive systems first-order PDEs called Friedrichs' systems.