SIAM Journal on Mathematical Analysis

We analyze the structure of trivariate C1 splines on uniform tetrahedral partitions $\Delta$. The Freudenthal partitions $\Delta$ are obtained from uniform cube partitions by using three planes with a common line to subdivide every cube into six ...

We prove the solution of the Navier--Stokes equations for one-dimensional compressible heat-conducting fluids with centered rarefaction data of small strength exists globally in time, and moreover, as the viscosity and heat-conductivity coefficients tend ...

We study the asymptotic behavior of energies of Ginzburg--Landau type, for maps from $\mathbb{R}^{n+k}$ into $\mathbb{R}^k$, and when the growth exponent p is strictly larger than k. We prove a compactness and $\Gamma$-convergence result, with respect to ...

We give results for the $\Gamma$-limit of a scaled elastic energy of a film as the thickness $h>0$ converges to zero. The elastic energy density models materials with multiple phases or variants and is thus nonconvex. The model includes an interfacial ...

We deal with the inverse scattering problem of determining the surface impedance of a partially coated obstacle. We prove a stability estimate of logarithmic type for the impedance term by the far field measurements.

The purpose of this paper is to study the solutions to the Signorini problem with Coulomb friction (the so-called Coulomb problem). Some optimal a priori estimates are given, and a uniqueness criterion is exhibited. Recently, nonuniqueness examples have ...

We study the scaling behavior of thin martensitic films. Specifically we consider an elastic energy with two SO(3) invariant wells which are strongly incompatible in the sense of Matos and Sverák, but whose two-dimensional projections may be compatible. ...

We consider the Hamilton--Jacobi equation \[ \partial_t u+H(x,Du)=0\qquad \hbox{in $(0,+\infty)\times\T^{N}$}, \] where $\T^{N}$ is the flat N-dimensional torus, and the Hamiltonian $H(x,p)$ is assumed continuous in x and strictly convex and coercive in p...

Certain liquids on solid substrates form a configuration of droplets connected by a precursor layer. This configuration coarsens: The average droplet size grows while the number of droplets decreases and the characteristic distance between them increases. ...

This paper is to construct Riesz wavelets with short support. Riesz wavelets with short support are the objective of interest in both theory and application. In theory, it is known that a B-spline of order m has the shortest support among all compactly ...

We discuss the well-posedness of a class of Neumann problems for n x n quasi-linear parabolic systems arising from models of sedimentation of polydisperse suspensions in engineering applications. This class of initial-boundary value problems includes the ...

In this paper we wish to present a new class of tight frames on the sphere. These frames have excellent pointwise localization and approximation properties. These properties are based on pointwise localization of kernels arising in the spectral calculus ...

This paper deals with a model for traffic flow based on a system of conservation laws [A. Aw and M. Rascle, SIAM J. Appl. Math., 60 (2000), pp. 916-938]. We construct a solution of the Riemann problem at an arbitrary junction of a road network. Our ...

We derive the high frequency limit of the Helmholtz equation with source term when the source is the sum of two point sources. We study it in terms of Wigner measures (quadratic observables). We prove that the Wigner measure associated with the solution ...

For one-dimensional kinetic BGK models, regarded as relaxation models for scalar conservation laws with genuinely nonlinear fluxes, existence of small amplitude traveling waves is proven. Dynamic stability of these kinetic shock profiles is shown by ...