Archive for Rational Mechanics and Analysis
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Directional Oscillations, Concentrations, and Compensated Compactness via Microlocal Compactness Forms
Archive for Rational Mechanics and Analysis - Tập 215 - Trang 1-63 - 2014
This work introduces microlocal compactness forms (MCFs) as a new tool to study oscillations and concentrations in L
p
-bounded sequences of functions. Decisively, MCFs retain information about the location, value distribution, and direction of oscillations and concentrations, thus extending at the same time the theories of (generalized) Young measures and H-measu......
Zur theorie elastischer schwingungen in inhomogenen medien
Archive for Rational Mechanics and Analysis - Tập 39 - Trang 158-168 - 1970
Quadratic inequalities and coefficient estimates for schlicht functions
Archive for Rational Mechanics and Analysis - - 1972
Weakly Nonlinear-Dissipative Approximations of Hyperbolic–Parabolic Systems with Entropy
Archive for Rational Mechanics and Analysis - Tập 201 - Trang 377-412 - 2011
Hyperbolic–parabolic systems have spatially homogenous stationary states. When the dissipation is weak, one can derive weakly nonlinear-dissipative approximations that govern perturbations of these constant states. These approximations are quadratically nonlinear. When the original system has an entropy, the approximation is formally dissipative in a natural Hilbert space. We show that when the ap......
Global Classical Solutions for Partially Dissipative Hyperbolic System of Balance Laws
Archive for Rational Mechanics and Analysis - Tập 211 - Trang 513-553 - 2013
The basic existence theory of Kato and Majda enables us to obtain local-in-time classical solutions to generally quasilinear hyperbolic systems in the framework of Sobolev spaces (in x) with higher regularity. However, it remains a challenging open problem whether classical solutions still preserve well-posedness in the case of critical regularity. This paper is concerned with partially dissipativ......
Crystal Dislocations with Different Orientations and Collisions
Archive for Rational Mechanics and Analysis - Tập 217 - Trang 231-261 - 2014
We study a parabolic differential equation whose solution represents the atom dislocation in a crystal for a general type of Peierls-Nabarro model with possibly long range interactions and an external stress. Differently from the previous literature, we treat here the case in which such dislocation is not the superposition of transitions all occurring with the same orientations (i.e. opposite orie......
Exact theory of stress and strain in rods and shells
Archive for Rational Mechanics and Analysis - Tập 1 - Trang 295-323 - 1957
A Locally Quadratic Glimm Functional and Sharp Convergence Rate of the Glimm Scheme for Nonlinear Hyperbolic Systems
Archive for Rational Mechanics and Analysis - Tập 196 - Trang 455-487 - 2009
Consider the Cauchy problem for a strictly hyperbolic, N × N quasilinear system in one space dimension
$$u_{t} \, + \, A(u)u_{x} = 0, \qquad u(0, x) = {\bar u}(x), \quad \quad \quad \quad (1)$$
where
$${{u \mapsto A(u)}}$$
......
A frame-independent description of the principles of classical mechanics
Archive for Rational Mechanics and Analysis - Tập 95 - Trang 1-22 - 1986
Relaxation Approximation and Asymptotic Stability of Stratified Solutions to the IPM Equation
Archive for Rational Mechanics and Analysis - Tập 248 - Trang 1-35 - 2023
We prove the nonlinear asymptotic stability of stably stratified solutions to the Incompressible Porous Media equation (IPM) for initial perturbations in
$$\dot{H}^{1-\tau }(\mathbb {R}^2) \cap \dot{H}^s(\mathbb {R}^2)$$
with
$$......
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