Local existence of quasispherical space–time initial data

Local existence of quasispherical space–time initial data

On the Existence of Spacetime Structure†

I examine the debate between substantivalists and relationalists about the ontological character of spacetime and conclude it is not well posed. I argue that the so-called Hole Argument does not bear on the debate, because it provides no clear criterion to distinguish the positions. I propose two such precise criteria and construct separate arguments based on each to yield contrary conclusions,...

Elastic Initial and Post-local Buckling of Profiled through Girders

An experiment investigating the elastic local buckling response of trough girders composed of thin profiled steel sheeting has been undertaken Beam tests were performed to promote initial local buckling in a region of constant moment in the elastic range of structural response. The results of the experiments were compared with an elastic complex semi-analytical finite strip method of analysis, ...

On the Existence of Spacetime Structure: Technical Appendices†

I sketch here the construction of Geroch (1969) (whose exposition I closely follow), which grounds the arguments of section 3 in Curiel (2016). (I simplify his construction in non-essential ways for our purposes, and gloss over unnecessary technicalities.) Consider a 1-parameter family of relativistic spacetimes, by which I mean a family {(Mλ, g(λ))}λ∈(0,1], where each (Mλ, g(λ)) is a relativis...

Local and Global Existence of Solutions to Semilinear Parabolic Initial Value Problems

This paper is devoted to establishing local and global existence theorems for autonomous semilinear parabolic initial value problems. The local existence theorems do not require Lipchitz condition on nonlinear term. The global existence theorem is an extension of the well-known result of Fujita-Weissler for semilinear heat equations to general autonomous semilinear parabolic equations and systems.