A Local Existence and Uniqueness Theorem for a K-BKZ-Fluid.

1983 ◽  
Author(s):  
Michael Renardy
Keyword(s):  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Existence And Uniqueness Theorem ◽  
Local Existence And Uniqueness

scholarly journals An abstract inverse problem

1991 ◽  
Vol 4 (2) ◽  
pp. 117-128 ◽  
Author(s):  
M. Choulli
Keyword(s):  
Inverse Problem ◽  
Uniqueness Theorem ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Continuous Solution ◽  
Local Existence ◽  
Sufficient Conditions ◽  
Existence And Uniqueness Theorem ◽  
Local Existence And Uniqueness ◽  
Abstract Integrodifferential Equation

In this paper we consider an inverse problem that corresponds to an abstract integrodifferential equation. First, we prove a local existence and uniqueness theorem. We also show that every continuous solution can be locally extended in a unique way. Finally, we give sufficient conditions for the existence and a stability of the global solution.

The Einstein equation for signature type changing spacetimes

1994 ◽  
Vol 446 (1926) ◽  
pp. 115-126 ◽  
Keyword(s):  
Scalar Field ◽  
Uniqueness Theorem ◽  
Einstein Equation ◽  
Existence And Uniqueness ◽  
Energy Momentum Tensor ◽  
Local Existence ◽  
Momentum Tensor ◽  
Existence And Uniqueness Theorem ◽  
Local Existence And Uniqueness ◽  
Type Change

We give a local existence and uniqueness theorem for solutions of Einstein’s equations with dust energy momentum tensor in the class of m -dimensional, analytic, transverse, signature type changing spacetimes where the initial condi­tions are given on the hypersurface of signature type change. We also prove a similar theorem in the case that the energy momentum tensor represents a scalar field.

scholarly journals ROUGH VOLTERRA EQUATIONS 1: THE ALGEBRAIC INTEGRATION SETTING

2009 ◽  
Vol 09 (03) ◽  
pp. 437-477 ◽  
Author(s):  
AURÉLIEN DEYA ◽  
SAMY TINDEL
Keyword(s):  
Brownian Motion ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Volterra Equations ◽  
Existence And Uniqueness Theorem ◽  
Hölder Exponent ◽  
Local Existence And Uniqueness ◽  
Hurst Coefficient ◽  
Rough Path ◽  
Driving Signal

We define and solve Volterra equations driven by an irregular signal, by means of a variant of the rough path theory called algebraic integration. In the Young case, that is for a driving signal with Hölder exponent γ > 1/2, we obtain a global solution, and are able to handle the case of a singular Volterra coefficient. In case of a driving signal with Hölder exponent 1/3 < γ < 1/2, we get a local existence and uniqueness theorem. The results are easily applied to the fractional Brownian motion with Hurst coefficient H > 1/3.

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