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Temperature-dependent hysteresis in one-dimensional thermovisco-elastoplasticity

Pavel Krejčí, Jürgen Sprekels (1998)

Applications of Mathematics

In this paper, we develop a thermodynamically consistent description of the uniaxial behavior of thermovisco-elastoplastic materials for which the total stress σ contains, in addition to elastic, viscous and thermic contributions, a plastic component σ p of the form σ p ( x , t ) = 𝒫 [ ε , θ ( x , t ) ] ( x , t ) . Here ε and θ are the fields of strain and absolute temperature, respectively, and { 𝒫 [ · , θ ] } θ > 0 denotes a family of (rate-independent) hysteresis operators of Prandtl-Ishlinskii type, parametrized by the absolute temperature. The system of momentum...

The Cauchy problem for systems through the normal form of systems and theory of weighted determinant

Waichiro Matsumoto (1998/1999)

Séminaire Équations aux dérivées partielles

The author propose what is the principal part of linear systems of partial differential equations in the Cauchy problem through the normal form of systems in the meromorphic formal symbol class and the theory of weighted determinant. As applications, he choose the necessary and sufficient conditions for the analytic well-posedness ( Cauchy-Kowalevskaya theorem ) and C ∞ well-posedness (Levi condition).

The Cauchy problem for the coupled Klein-Gordon-Schrödinger system

Changxing Miao, Youbin Zhu (2006)

Annales Polonici Mathematici

We consider the Cauchy problem for a generalized Klein-Gordon-Schrödinger system with Yukawa coupling. We prove the existence of global weak solutions by the compactness method and, through a special choice of the admissible pairs to match two types of equations, we prove the uniqueness of those solutions by an approach similar to the method presented by J. Ginibre and G. Velo for the pure Klein-Gordon equation or pure Schrödinger equation. Though it is very simple in form, the method has an unnatural...

The existence and uniqueness theorem in Biot's consolidation theory

Alexander Ženíšek (1984)

Aplikace matematiky

Existence and uniqueness theorem is established for a variational problem including Biot's model of consolidation of clay. The proof of existence is constructive and uses the compactness method. Error estimates for the approximate solution obtained by a method combining finite elements and Euler's backward method are given.

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