By Morton E. Gurtin
ISBN-10: 0898711681
ISBN-13: 9780898711684
Finite elasticity is a concept of elastic fabrics which are able to present process huge deformations. This conception is inherently nonlinear and is mathematically fairly advanced. This monograph offers a derivation of the fundamental equations of the speculation, a dialogue of the overall boundary-value difficulties, and a remedy of a number of fascinating and significant distinct subject matters resembling easy shear, area of expertise, the tensile deformations of a dice, and antiplane shear. The monograph is meant for engineers, physicists, and mathematicians.
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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.
Topics in Finite Elasticity by Morton E. Gurtin
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