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Shock waves --- Reaction-diffusion equations --- Reaction-diffusion equations.

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This monograph presents a self contained mathematical treatment of the initial value problem for shock wave solutions of the Einstein equations in General Relativity. The first two chapters provide background for the introduction of a locally intertial Glimm Scheme, a non-dissipative numerical scheme for approximating shock wave solutions of the Einstein equations in spherically symmetric spacetimes. What follows is a careful analysis of this scheme providing a proof of the existence of (shock wave) solutions of the spherically symmetric Einstein equations for a perfect fluid, starting from initial density and velocity profiles that are only locally of bounded total variation. The book covers the initial value problems for Einstein's gravitational field equations with fluid sources and shock wave initial data. It has a clearly outlined goal: proving a certain local existence theorem. Concluding remarks are added and commentary is provided throughout. The book will be useful to graduate students and researchers in mathematics and physics.

Einstein field equations. --- Shock waves. --- Shock (Mechanics) --- Waves --- Einstein's field equations --- Einstein's gravitational field equations --- Einstein's law of gravitation --- Field equations, Einstein --- Differential equations --- Field theory (Physics) --- General relativity (Physics) --- Gravitational fields --- Mathematics. --- Applications of Mathematics. --- Classical and Quantum Gravitation, Relativity Theory. --- Math --- Science --- Applied mathematics. --- Engineering mathematics. --- Gravitation. --- Engineering --- Engineering analysis --- Mathematical analysis --- Matter --- Physics --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Mathematics --- Properties

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This monograph presents a self contained mathematical treatment of the initial value problem for shock wave solutions of the Einstein equations in General Relativity. The first two chapters provide background for the introduction of a locally intertial Glimm Scheme, a non-dissipative numerical scheme for approximating shock wave solutions of the Einstein equations in spherically symmetric spacetimes. What follows is a careful analysis of this scheme providing a proof of the existence of (shock wave) solutions of the spherically symmetric Einstein equations for a perfect fluid, starting from initial density and velocity profiles that are only locally of bounded total variation. The book covers the initial value problems for Einstein's gravitational field equations with fluid sources and shock wave initial data. It has a clearly outlined goal: proving a certain local existence theorem. Concluding remarks are added and commentary is provided throughout. The book will be useful to graduate students and researchers in mathematics and physics.

Mathematics --- Cosmology --- Astrophysics --- Theory of relativity. Unified field theory --- astrofysica --- toegepaste wiskunde --- relativiteitstheorie --- kosmologie