Modeling of CollisionsEditions Scientifiques et Medicales Elsevier, 1998 - 222 من الصفحات |
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الصفحة 194
... Theorem 18.1 Let -x≤ T1≤ 0≤T2≤∞ . Then n Є Cò ( Rt ; M * ( Rd ) w- * ) , u € L∞ ( Rt ; L1 ( Ra ; dn ( t ) ) d ) ... Theorem 18.1 ) . Theorem 18.1 yields : Corollary 18.1 Let uЄ C ( Rd ) and let -∞ ≤ T1 ≤ 0 be an interval on which ...
... Theorem 18.1 Let -x≤ T1≤ 0≤T2≤∞ . Then n Є Cò ( Rt ; M * ( Rd ) w- * ) , u € L∞ ( Rt ; L1 ( Ra ; dn ( t ) ) d ) ... Theorem 18.1 ) . Theorem 18.1 yields : Corollary 18.1 Let uЄ C ( Rd ) and let -∞ ≤ T1 ≤ 0 be an interval on which ...
الصفحة 203
... Theorem 19.1 Assume A1 , A2 , A3 . Then for j = a ) the functional E has a minimizer ø1⁄2 in Cž , b ) there exist E , Є R ( in fact , E2 = E3 = 0 ) , such that the pair ( Ej , 45 ) solves ( 19.3 ) , c ) the minimizers 1.5 are unique up ...
... Theorem 19.1 Assume A1 , A2 , A3 . Then for j = a ) the functional E has a minimizer ø1⁄2 in Cž , b ) there exist E , Є R ( in fact , E2 = E3 = 0 ) , such that the pair ( Ej , 45 ) solves ( 19.3 ) , c ) the minimizers 1.5 are unique up ...
الصفحة 212
... Theorem 20.1 and Theorem 20.2 . There are however uniform estimates on no log no , o po log po available so the following compactness - by - convexity argument applies : 00 Ολ Lemma 20.3 Let C Rd , d € N , be a bounded domain and let G ...
... Theorem 20.1 and Theorem 20.2 . There are however uniform estimates on no log no , o po log po available so the following compactness - by - convexity argument applies : 00 Ολ Lemma 20.3 Let C Rd , d € N , be a bounded domain and let G ...
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atomic species BBGKY hierarchy Boltzmann Equation Braginskii charge classical collision frequencies collision integrals collision operator collision terms collisional conservation equation Coulomb logarithms Debye length defined diffusion distribution function electric field electron-ion energy equation Enskog equal mass ions equation set equilibrium fluid equations Fokker-Planck Galilean invariance gives heat flux heavy ions hydrodynamic interaction interdiffusion ion species ionic kinetic Landau Lemma limit linear magnetic field Maxwellian distributions Maxwellian estimate mean velocity multi-fluid equations neutral plasma numerical obtained Ohm's law particle Perthame perturbation calculation perturbation equations Phys Plasma Physics quantum Quantum Hydrodynamics Raß relative velocity scalar self-collision T₁ tensor Theorem thermal transport coefficients transport equations U₂ vector viscosity Vlasov Equation Wigner Yaß αβ მა