Initial boundary value problems for the displacement in an isothermal, viscous gas

DOI10.1016/0362-546X(90)90002-XzbMath0724.35066OpenAlexW2001389130MaRDI QIDQ5758577

Kenneth L. jun. Kuttler

Publication date: 1990

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(90)90002-x

zbMATH Keywords

existenceuniquenessinitial boundary value problems

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Gas dynamics (general theory) (76N15) Hyperbolic conservation laws (35L65)

Related Items (7)

Velocity dependent boundary conditions for the displacement in a one dimensional viscoelastic material ⋮ ON THE STABILIZATION OF A VISCOUS BAROTROPIC SELF-GRAVITATING MEDIUM WITH A NONMONOTONE EQUATION OF STATE ⋮ Regularity of the displacement in a one-dimensional viscoelastic material ⋮ Stabilization for equations of one-dimensional viscous compressible heat-conducting media with nonmonotone equation of state. ⋮ Corrections to: The one-dimensional displacement in an isothermal viscous compressible fluid with a nonmonotone equation of state ⋮ Remark on the stabilization of a viscous barotropic medium with a nonmonotonic equation of state ⋮ The one-dimensional displacement in an isothermal viscous compressible fluid with a nonmonotone equation of state

Cites Work

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• Phase transitions in one-dimensional nonlinear viscoelasticity: Admissibility and stability
• Asymptotic behaviour and changes of phase in one-dimensional nonlinear viscoelasticity
• Asymptotic behaviour of the density for one-dimensional Navier-Stokes equations
• 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
• On the exponential stability of solutions of \(E(u_ x)u_{xx} + \lambda u_{xtx} = \rho u_{tt}\)
• Time-dependent implicit evolution equations
• Weak solutions of initial-boundary value problems for class of nonlinear viscoelastic equations
• Initial-boundary value problems for the equation 𝑢_{𝑡𝑡}=(𝜎(𝑢ₓ))ₓ+(𝛼(𝑢ₓ)𝑢_{𝑥𝑡})ₓ+𝑓
• On the existence of solutions to the equation \(u_{tt}=u_{xxt}+\sigma (u_x)_x\)

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