Gauss-Ostrogradsky theorem

Using the Gauss-Ostrogradsky theorem, Eq. (3.69) can be written over the entire volume... 

Nonequilibrium thermodynamics often uses the Gauss-Ostrogradsky theorem, which states that the flux of a vector through a surface a is equal to the volume integral of the divergence of the vector v for the space of volume Fbounded by that surface... 

Since we are approaching a problem of current and potential distributions, we have to consider the Gauss-Ostrogradsky theorem for the electric field, E ... 

Recall the two important equations before we start to discuss the conservation laws. The first one is the Gauss-Ostrogradsky theorem . It relates the surface and volume integrals of the type... 

Applying the Gauss-Ostrogradsky theorem (5.1) to the integral in the right part of (5.7) and using (5.8), we obtain... 

Applying to (5.79) the Gauss-Ostrogradsky theorem and using expressions... 

The first term on the right-hand side of Eq. (1.88) can be transformed by using the Gauss-Ostrogradsky theorem for the vector gradient ... 

Equation (P4.3.4), known as the Gauss-Ostrogradsky, or divergence, theorem, is usually written... 

The Gauss theorem is also known as the divergence theorem. Green s theorem, and Ostrogradsky s theorem [36]. In particular, the vector form of Gauss s theorem is normally referred to as the divergence theorem [18]. 

I retain tfie original terminology here. In Russian scientific literature, the Gauss s theorem is called the Gauss-Ostrogradsky dieorem. — VF... 

The second important relationship is the Greetf-Ostrogradsky theorem, or the divergence theorem (also called the Gauss theorem, but this leads to confusion with a similar theorem bearing the same name in electrostatics seen in case study B5) ... 

The other way to calculate the volume inside the triangulated surface is to use the Ostrogradski-Gauss theorem. It relates the surface integral from a vector field j to a volume integral from its divergence ... 

Integrating equation (9) over and applying the Ostrogradsky-Gauss theorem yields [24c]... 

The divergence theorem is also known as Gauss theorem and Ostn padsky s theorem (named after the Russian mathematician Michel Ostrogradsky (1801-61), who stated it in 1831). Gauss law for electric fields is a parriculm case of the divergence theorem. 

Making use of a divergence theorem for curved surfaces due to Green, Gauss, and Ostrogradsky (cf. Weatherburn [28]), we obtain ... 

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