Group analysis and linearization procedure for a nonautonomous model describing rate-type materials

DOI10.1063/1.530215zbMath0774.73030OpenAlexW2060655947MaRDI QIDQ4201708

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Publication date: 6 September 1993

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.530215

zbMATH Keywords

boundary value problemssimilarity solutionssimilarity reductioninitial boundary problemsmaterial response function\(2\times 2\) quasilinear system

Mathematics Subject Classification ID

Geometric theory, characteristics, transformations in context of PDEs (35A30) Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) (74D99)

Related Items (4)

Double-wave solutions to quasilinear hyperbolic systems of first-order PDEs ⋮ Linearization of nonautonomous models describing fluid filled elastic tubes and nonlinear elastic rods with variable cross-section ⋮ Finite Time Stabilization of Nonautonomous First-Order Hyperbolic Systems ⋮ Bounded and almost periodic solvability of nonautonomous quasilinear hyperbolic systems

Cites Work

• Linearization of a hyperbolic model for non-linear heat conduction through hodograph-like and Bäcklund transformation
• Complete exceptionality, constitutive laws and symmetric form for a nonlinear inelastic rod
• Some exact solutions for wave propagation in viscoelastic, viscoplastic and electrical transmission lines
• Exact Solutions for Large Amplitude Waves in Dispersive and Dissipative Systems
• Some Applications of the Riemann Method to Electromagnetic Wave Propagation in Nonlinear Media
• A class of linearizable models and generation of material response functions to nonlinear hyperbolic heat conduction

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