Weak and Young Measure Solutions for Hyperbolic Initial Boundary Value Problems of Elastodynamics in the Orlicz--Sobolev Space Setting
From MaRDI portal
Publication:2798650
DOI10.1137/15M1016138zbMath1338.35302MaRDI QIDQ2798650
Nguyêñ Hôǹg Thái, Dariusz Pączka
Publication date: 13 April 2016
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
nonlinear elastodynamicsnonlinear viscoelasticitynonconvex energyconvex energynonstandard growth nonlinearity
Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Nonlinear elasticity (74B20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Nonlinear constitutive equations for materials with memory (74D10) Spaces of measures, convergence of measures (28A33) Weak solutions to PDEs (35D30) Existence of solutions of dynamical problems in solid mechanics (74H20) Second-order quasilinear hyperbolic equations (35L72)
Related Items (5)
A pocket guide to nonlinear differential equations in Musielak-Orlicz spaces ⋮ On steady flow of non-Newtonian fluids with frictional boundary conditions in reflexive Orlicz spaces ⋮ Frictional Contact Problems for Steady Flow of Incompressible Fluids in Orlicz Spaces ⋮ Effective energy integral functionalsfor thin films on curl-free vector fields in the Orlicz–Sobolev space setting ⋮ Newton's second law with a semiconvex potential
Cites Work
- Korn type inequalities in Orlicz spaces
- Quasilinear elliptic non-homogeneous Dirichlet problems through Orlicz-Sobolev spaces
- On quasilinear parabolic equations in the Orlicz spaces
- Strongly nonlinear parabolic equations with natural growth terms in Orlicz spaces
- Compactness of integral operators in Banach function spaces
- Approximation of quasiconvex functions, and lower semicontinuity of multiple integrals
- Phase transitions in one-dimensional nonlinear viscoelasticity: Admissibility and stability
- Asymptotic behaviour and changes of phase in one-dimensional nonlinear viscoelasticity
- Lectures on the Ekeland variational principle with applications and detours. Lectures delivered at the Indian Institute of Science, Bangalore, India under the T.I.F.R.-I.I.Sc. programme in applications of mathematics
- Multivalued superposition operators in ideal spaces of vector functions. II
- On continuity of the imbedding operation from \(W^k_{M_1}(\Omega)\) into \(W^k_{M_2}(|Omega)\)
- Energy minimization and the formation of microstructure in dynamic anti- plane shear
- On principal eigenvalues for quasilinear elliptic differential operators: an Orlicz-Sobolev space setting
- On the dynamics of fine structure
- Parametrized measures and variational principles
- Young measure solutions for nonlinear evolutionary systems of mixed type
- Ideal spaces
- On Banach function \(M\)-spaces
- Weak solutions for a class of nonlinear systems of viscoelasticity
- The parabolic-hyperbolic system governing the spatial motion of nonlinearly viscoelastic rods
- Existence theorems for boundary value problems for strongly nonlinear elliptic systems
- Regularity of quasiconvex envelopes
- Inhomogeneous Orlicz-Sobolev spaces and nonlinear parabolic initial value problems
- Espaces de traces des espaces de Sobolev-Orlicz
- Eigenvalue problems in Orlicz-Sobolev spaces for rapidly growing operators in divergence form
- On generalized solutions of two-phase flows for viscous incompressible fluids
- A local existence result for a system of viscoelasticity with physical viscosity
- Orlicz-Sobolev spaces and imbedding theorems
- Quasilinear elliptic equations in \(\mathbb{R }^{N}\) via variational methods and Orlicz-Sobolev embeddings
- On one extension theorem dealing with weighted Orlicz-Slobodetskii space. Analysis on Lipschitz subgraph and Lipschitz domain
- Convergence of a Full Discretization of Quasi-linear Parabolic Equations in Isotropic and Anisotropic Orlicz Spaces
- Some Open Problems in Elasticity
- A General Approach to Lower Semicontinuity and Lower Closure in Optimal Control Theory
- Existence Theorems for the Dirichlet Elliptic Inclusion Involving Exponential-Growth-Type Multivalued Right-Hand Side
- The Young Measure Representation for Weak Cluster Points of Sequences in M-spaces of Measurable Functions
- Weak Convergence of Integrands and the Young Measure Representation
- Dynamical modelling of phase transitions by means of viscoelasticity in many dimensions
- An existence theorem for a strongly nonlinear elliptic problem in Orlicz spaces
- Implicit Time Discretization and Global Existence for a Quasi-Linear Evolution Equation with Nonconvex Energy
- Variational Analysis
- Young Measure Solutions for Nonconvex Elastodynamics
- Semicontinuity and continuous selections for the multivalued superposition operator without assuming growth-type conditions
- Young Measure Solutions for a Nonlinear Parabolic Equation of Forward-Backward Type
- Traces of Orlicz‐Sobolev functions under general growth restrictions
- The Euler–Lagrange inclusion in Orlicz–Sobolev spaces
- Young-Measure approximations for elastodynamics with non-monotone stress-strain relations
- Nonlinear Elliptic Boundary Value Problems for Equations With Rapidly (Or Slowly) Increasing Coefficients
- Nonlinear problems of elasticity
- On the existence of solutions to the equation \(u_{tt}=u_{xxt}+\sigma (u_x)_x\)
- A variational approximation scheme for three-dimensional elastodynamics with polyconvex energy
- Orlicz-Sobolev boundary trace embeddings
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Weak and Young Measure Solutions for Hyperbolic Initial Boundary Value Problems of Elastodynamics in the Orlicz--Sobolev Space Setting
