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... 

It is easy to apply the Ostrogradsky theorem for deriving the entropy fluxes and the thermodynamic forces that initiate these fluxes. In fact, the balance of entropy (it also is an extensive parameter, S = ps) is... 

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... 

After the transient period, the molar flux perpendicular to the interface between the conductor and the insulating media equals zero. By applying the Ostrogradsky theorem ", it is possible to deduce that the charge flow rate is the same in all sections of the conductor, whether perpendicular to the current density or not, as shown in figure4.3 ... 

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

This equation is referred in mathematics as the Ostrogradski theorem, from which an important expression originates ... 

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]... 

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 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 ... 

S is the closed surface surrounding V and n is the outward normal to the domain on that surface (Figure 1.1). Following Ostrogradsky s theorem, and then using (equation [1.39]), we arrive at ... 

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