Dynamical modelling of phase transitions by means of viscoelasticity in many dimensions
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Publication:4021237
DOI10.1017/S0308210500014177zbMath0758.73004MaRDI QIDQ4021237
Publication date: 16 January 1993
Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)
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Related Items (29)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Quasiconvexity at the boundary, positivity of the second variation and elastic stability
- Convergence of approximate solutions to conservation laws
- A model for twinning
- Fine phase mixtures as minimizers of energy
- Phase transitions in one-dimensional nonlinear viscoelasticity: Admissibility and stability
- On global regular solutions of third order partial differential equations
- Geometric theory of semilinear parabolic equations
- On the mathematical foundations of elastic stability theory. I
- Asymptotic behaviour and changes of phase in one-dimensional nonlinear viscoelasticity
- Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity
- Systems of nonlinear wave equations with nonlinear viscosity
- Stability for semilinear parabolic equations with noninvertible linear operator
- On the asymptotic behaviour of the Green operators for elliptic boundary problems and the pure imaginary powers of some second order operators
- On the existence, uniqueness, and stability of solutions of the equation \(p_0 {\mathfrak X}_{tt} = E({\mathfrak X}_ x) {\mathfrak X}_{xx} +\lambda {\mathfrak X}_{xxt}\)
- The mixed initial-boundary value problem for the equations of nonlinear one-dimensional viscoelasticity
- Quasi-convexity and the lower semicontinuity of multiple integrals
- Some remarks concerning quasiconvexity and strong convergence
- Existence of solutions for a mathematical model of structural phase transitions in shape memory alloys
- Weakly Differentiable Functions
- Initial-boundary value problems for the equation 𝑢_{𝑡𝑡}=(𝜎(𝑢ₓ))ₓ+(𝛼(𝑢ₓ)𝑢_{𝑥𝑡})ₓ+𝑓
- Existence Theorems for a Quasilinear Evolution Equation
- Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
- Semicontinuity problems in the calculus of variations
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