Let X,Y, Z be Banach spaces and let u : X×Y → Z be a bounded bilinear map. Given a locally compact abelian group G , and two functions f ∈ L(G,X) and g ∈ L(G,Y ), we define the u -convolution of f and g as the Z -valued function f ∗u g(t) = ∫ G u(f(t− s), g(s))dμG(s) where dμG stands for the Haar measure on G . We define the concepts of vector-valued approximate identity and summability kernel ...

We consider the equations of stationary, incompressible magnetohydrodynamics posed in a bounded domain in three dimensions and treat the full, coupled system of equations with inhomogeneous boundary conditions. Under certain conditions on the data, we show that the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed. We discuss a finite element disc...

For the p-system with large BV initial data, an assumption introduced in [3] by Bakhvalov guarantees the global existence of entropy weak solutions with uniformly bounded total variation. The present paper provides a partial converse to this result. Whenever Bakhvalov’s condition does not hold, we show that there exist front tracking approximate solutions, with uniformly positive density, whose...

The ordering principle states that every finite linear order has a least element. We show that, in the relativized setting, the surjective weak pigeonhole principle for polynomial time functions does not prove a Herbrandized version of the ordering principle over T 2 . This answers an open question raised in [Buss, Ko lodziejczyk and Thapen, 2012] and completes their program to compare the stre...

A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over bounded volumes that have smooth boundaries in three dimensions is described. key aspect of this approach it allows the user to approximate value integral without explicit knowledge an expression boundary surface. Instead, a tesselation node set utilized inform algorithm domai...