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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 54
  3. Calculus of Variations and Partial Differential Equations : Volume 54, Issue 4, December 2015
  4. On the almost periodic homogenization of non-linear scalar conservation laws
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Calculus of Variations and Partial Differential Equations : Volume 56
Calculus of Variations and Partial Differential Equations : Volume 55
Calculus of Variations and Partial Differential Equations : Volume 54
Calculus of Variations and Partial Differential Equations : Volume 54, Issue 4, December 2015
On a general SU(3) Toda system
Conformal metrics in $$\mathbb {R}^{2m}$$ with constant Q-curvature and arbitrary volume
On the growth of solutions to the minimal surface equation over domains containing a halfplane
Transport distances and geodesic convexity for systems of degenerate diffusion equations
Ambrosetti–Prodi-type problems for quasi-linear elliptic equations with nonlocal boundary conditions
Boundary singularities of positive solutions of quasilinear Hamilton–Jacobi equations
A bifurcation phenomenon in a singularly perturbed one-phase free boundary problem of phase transition
$$\varepsilon $$ -regularity for systems involving non-local, antisymmetric operators
$$C^{\sigma +\alpha }$$ regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels
On length-preserving and area-preserving nonlocal flow of convex closed plane curves
On the almost periodic homogenization of non-linear scalar conservation laws
Characterization of n-rectifiability in terms of Jones’ square function: part I
Singular points of Hölder asymptotically optimally doubling measures
Parabolic complex Monge–Ampère type equations on closed Hermitian manifolds
Variational properties of the first curve of the Fučík spectrum for elliptic operators
Resonance identities and stability of symmetric closed characteristics on symmetric compact star-shaped hypersurfaces
Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity
A free boundary problem arising in PDE optimization
Sharp asymptotic estimates for eigenvalues of Aharonov-Bohm operators with varying poles
Boundary value problems for Willmore curves in $$\mathbb {R}^2$$
Global estimates for quasilinear parabolic equations on Reifenberg flat domains and its applications to Riccati type parabolic equations with distributional data
On a variational problem associated with a Hardy type inequality involving a mean oscillation
A sharp quantitative isoperimetric inequality in hyperbolic n-space
A rigidity theorem for codimension one shrinking gradient Ricci solitons in $${\mathbb {R}}^{n+1}$$
Uniqueness of positive bound states with multi-bump for nonlinear Schrödinger equations
Existence and multiplicity of self-similar solutions for heat equations with nonlinear boundary conditions
Bending of thin periodic plates
Solutions concentrating around the saddle points of the potential for critical Schrödinger equations
Extremal and sign-changing solutions of supercritical logistic-type equations in $$\mathbb {R}^N$$
Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians
Calculus of Variations and Partial Differential Equations : Volume 54, Issue 3, November 2015
Calculus of Variations and Partial Differential Equations : Volume 54, Issue 2, October 2015
Calculus of Variations and Partial Differential Equations : Volume 54, Issue 1, September 2015
Calculus of Variations and Partial Differential Equations : Volume 53
Calculus of Variations and Partial Differential Equations : Volume 52
Calculus of Variations and Partial Differential Equations : Volume 51
Calculus of Variations and Partial Differential Equations : Volume 50
Calculus of Variations and Partial Differential Equations : Volume 49
Calculus of Variations and Partial Differential Equations : Volume 48
Calculus of Variations and Partial Differential Equations : Volume 47
Calculus of Variations and Partial Differential Equations : Volume 46
Calculus of Variations and Partial Differential Equations : Volume 45
Calculus of Variations and Partial Differential Equations : Volume 44
Calculus of Variations and Partial Differential Equations : Volume 43
Calculus of Variations and Partial Differential Equations : Volume 42
Calculus of Variations and Partial Differential Equations : Volume 41
Calculus of Variations and Partial Differential Equations : Volume 40
Calculus of Variations and Partial Differential Equations : Volume 39
Calculus of Variations and Partial Differential Equations : Volume 38
Calculus of Variations and Partial Differential Equations : Volume 37
Calculus of Variations and Partial Differential Equations : Volume 36
Calculus of Variations and Partial Differential Equations : Volume 35
Calculus of Variations and Partial Differential Equations : Volume 34
Calculus of Variations and Partial Differential Equations : Volume 33
Calculus of Variations and Partial Differential Equations : Volume 32
Calculus of Variations and Partial Differential Equations : Volume 31
Calculus of Variations and Partial Differential Equations : Volume 30
Calculus of Variations and Partial Differential Equations : Volume 29
Calculus of Variations and Partial Differential Equations : Volume 28
Calculus of Variations and Partial Differential Equations : Volume 27
Calculus of Variations and Partial Differential Equations : Volume 26
Calculus of Variations and Partial Differential Equations : Volume 25
Calculus of Variations and Partial Differential Equations : Volume 24
Calculus of Variations and Partial Differential Equations : Volume 23
Calculus of Variations and Partial Differential Equations : Volume 22
Calculus of Variations and Partial Differential Equations : Volume 21
Calculus of Variations and Partial Differential Equations : Volume 20
Calculus of Variations and Partial Differential Equations : Volume 19
Calculus of Variations and Partial Differential Equations : Volume 18
Calculus of Variations and Partial Differential Equations : Volume 17
Calculus of Variations and Partial Differential Equations : Volume 16
Calculus of Variations and Partial Differential Equations : Volume 15
Calculus of Variations and Partial Differential Equations : Volume 14
Calculus of Variations and Partial Differential Equations : Volume 13
Calculus of Variations and Partial Differential Equations : Volume 12
Calculus of Variations and Partial Differential Equations : Volume 11
Calculus of Variations and Partial Differential Equations : Volume 10
Calculus of Variations and Partial Differential Equations : Volume 9
Calculus of Variations and Partial Differential Equations : Volume 8
Calculus of Variations and Partial Differential Equations : Volume 7
Calculus of Variations and Partial Differential Equations : Volume 6
Calculus of Variations and Partial Differential Equations : Volume 5

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On the almost periodic homogenization of non-linear scalar conservation laws

Content Provider SpringerLink
Author Silva, Jean
Copyright Year 2015
Abstract The paper deals with the homogenization problem of non-linear scalar conservations laws $$\partial _t u_\varepsilon + \nabla _x\cdot (a(\frac{x}{\varepsilon })f(u_\varepsilon ))=0$$ . The vector field a is assumed to be incompressible and its components are assumed to be almost periodic. We prove that the weak limit of the family $$\{u_{\varepsilon }{\}}_{\varepsilon >0}$$ is the mean value of a function, which we call U(z, x, t), that is the entropy solution of a similar conservation law in the macroscopic variables, but with coefficients depending on the microscopic variables and has the property that the function $$z\mapsto \int _{\mathbb {R}_+^{n+1}}U(z,x,t)\varphi (x,t)\,dx\,dt$$ is also almost periodic for any $$\varphi \in C_c(\mathbb {R}_+^{n+1})$$ .
Ending Page 3641
Page Count 19
Starting Page 3623
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 4
Volume Number 54
Language English
Publisher Springer Berlin Heidelberg
Publisher Date 2015-08-25
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Conservation laws Stability Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Theoretical, Mathematical and Computational Physics Asymptotic behavior of solutions Nonlinear parabolic equations
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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