New PDF release: New Directions in Mathematical Fluid Mechanics: The

By Andrei V. Fursikov, Giovanni P. Galdi, Vladislav V. Pukhnachev

ISBN-10: 3034601514

ISBN-13: 9783034601511

The medical pursuits of Professor A.V. Kazhikhov have been essentially dedicated to Mathematical Fluid Mechanics, the place he completed amazing effects that had, and now have, an important impression in this field.

This quantity, devoted to the reminiscence of A.V. Kazhikhov, provides the most recent contributions from well known global experts in a couple of new vital instructions of Mathematical Physics, usually of Mathematical Fluid Mechanics, and, extra often, within the box of nonlinear partial differential equations. those effects are more often than not on the topic of boundary price difficulties and to manage difficulties for the Navier-Stokes equations, and for equations of warmth convection. different vital themes contain non-equilibrium techniques, Poisson-Boltzmann equations, dynamics of elastic physique, and comparable difficulties of functionality concept and nonlinear analysis.

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Additional resources for New Directions in Mathematical Fluid Mechanics: The Alexander V. Kazhikhov Memorial Volume (Advances in Mathematical Fluid Mechanics)

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Appl. 242 (2000), 191–211. C. Yu. Imanuvilov, Analysis of Neumann boundary optimal control problems for the stationary Boussinesq equations including solid media. SIAM J. Contr. Opt. 39 (2000), 457–477. [7] A. Capatina, R. Stavre, A control problem in bioconvective flow. J. Math. Kyoto Univ. 37 (1998), 585–595. V. Alekseev, Solvability of inverse extremum problems for stationary equations of heat and mass transfer. Sib. Math. J. V. Alekseev, Inverse extremal problems for stationary equations in mass transfer theory.

7) with the constants m, C being dependent on θ. By the last reason we will derive estimates in Lp -spaces which are independent of the parameter θ. First we prove the following lemma. Lemma 6.

Theorem 1. e. e. e. 13) hold for any function ψ ∈ T F (v). Here we define the set of test functions T F (v), related with the function v = v(x, t) ∈ C(Ω × [0, T ]) as T F (v) := {ϕ ∈ C 1,1 (Ω × [0, T ]) : ϕ(·, T ) = 0 on Ω and ϕ(x, t) = 0 on Γ∗T (v)}, where Γ∗T (v) := {(x, t) ∈ ΓT : (v · n)(x, t) 0}. Remark 1. 7), because we do not know beforehand Γ− T (v), the entrance of the flux of vortices into Ω, we have been compelled to introduce a set of test functions T F (v) depending on the solution v.

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New Directions in Mathematical Fluid Mechanics: The Alexander V. Kazhikhov Memorial Volume (Advances in Mathematical Fluid Mechanics) by Andrei V. Fursikov, Giovanni P. Galdi, Vladislav V. Pukhnachev


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