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.

four explicit finite difference schemes, including lax-friedrichs, nessyahu-tadmor, lax-wendroff and lax-wendroff with a nonlinear filter are applied to solve water hammer equations. the schemes solve the equations in a reservoir-pipe-valve with an instantaneous and gradual closure of the valve boundary. the computational results are compared with those of the method of characteristics (moc), a...

All finite element methods, as well much of the Hilbert-space theory for partial differential equations, rely on variational formulations, that is, problems type: find u?V such a(v,u)=l(v) each v?L, where V,L are Sobolev spaces. However, systems Friedrichs type, there is a sharp disparity between established well-posedness theories, which not variational, and very successful discontinuous Galer...

Certain Friedrichs systems can be posed on Hilbert spaces normed with a graph norm. Functions in such spaces arising from advective problems are found to have traces with a weak continuity property at points where the inflow and outflow boundaries meet. Motivated by this continuity property, an explicit space-time finite element scheme of the tent pitching type, with spaces that conform to the ...