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EXISTENCE AND UNIQUENESS OF SOLUTIONS TO THE FERMI-DIRAC BOLTZMANN EQUATION FOR SOFT POTENTIALS

期刊: QUARTERLY OF APPLIED MATHEMATICS, 2023; ()

In this paper we consider a modified quantum Boltzmann equation with the quantum effect measured by a continuous parameter delta that can decrease fro......

EXCITATION OF A LAYERED SPHERE BY N ACOUSTIC SOURCES: EXACT SOLUTIONS, LOW-FREQUENCY APPROXIMATIONS, AND INVERSE PROBLEMS

期刊: QUARTERLY OF APPLIED MATHEMATICS, 2023; 81 (1)

Acoustic excitation of a layered sphere by N external and internal point sources is considered. The direct problem is solved by developing a T-Matrix ......

STEADY PRANDTL LAYER EXPANSIONS WITH EXTERNAL FORCING

期刊: QUARTERLY OF APPLIED MATHEMATICS, 2023; 81 (2)

In this article we apply the machinery developed by Guo and Iyer [Valid-ity of Steady Prandtl Layer Expansions, Comm. Pure Appl. Math. (to appear) (20......

MATRIX-SCALED RESILIENT CONSENSUS OF DISCRETE-TIME AND CONTINUOUS-TIME NETWORKS

期刊: QUARTERLY OF APPLIED MATHEMATICS, 2023; 81 (4)

This paper studies the matrix-scaled resilient consensus problems over multi-agent networks as occurring in computer science and distributed control. ......

MINIMAL ENTROPY CONDITIONS FOR SCALAR CONSERVATION LAWS WITH GENERAL CONVEX FLUXES

期刊: QUARTERLY OF APPLIED MATHEMATICS, 2023; 81 (3)

We are concerned with the minimal entropy conditions for one-dimensional scalar conservation laws with general convex flux functions. For such scalar ......

SMOOTH SELF-SIMILAR IMPLODING PROFILES TO 3D COMPRESSIBLE EULER

期刊: QUARTERLY OF APPLIED MATHEMATICS, 2023; 81 (3)

The aim of this note is to present the recent results by Buckmaster, Cao-Labora, and Gomez-Serrano [Smooth imploding solutions for 3D compressible flu......

GLOBAL STABILITY OF ALMOST PERIODIC SOLUTIONS IN POPULATION DYNAMICS

期刊: QUARTERLY OF APPLIED MATHEMATICS, 2023; 81 (4)

We study first order differential equations with continuous almost periodic time dependence. We propose existence and global stability criteria of alm......

A CAUSAL FORMULATION OF DISSIPATIVE RELATIVISTIC FLUID DYNAMICS WITH OR WITHOUT DIFFUSION

期刊: QUARTERLY OF APPLIED MATHEMATICS, 2023; 81 (3)

The article proposes a causal five-field formulation of dissipative relativistic fluid dynamics as a quasilinear symmetric hyperbolic system of second......

LONG TIME GYROKINETIC EQUATIONS

期刊: QUARTERLY OF APPLIED MATHEMATICS, 2023; ()

The aim of this text is to elucidate the oscillating patterns (see C. Cheverry [Res. Rep. Math. (2018)]) which are generated in a toroidal plasma by a......

DISPERSIVE SHOCKS IN DIFFUSIVE-DISPERSIVE APPROXIMATIONS OF ELASTICITY AND QUANTUM-HYDRODYNAMICS

期刊: QUARTERLY OF APPLIED MATHEMATICS, 2023; 81 (3)

The aim is to assess the combined effect of diffusion and dispersion on shocks in the moderate dispersion regime. For a diffusive dispersive approxima......

DAMPED AND DRIVEN BREATHERS AND METASTABILITY

期刊: QUARTERLY OF APPLIED MATHEMATICS, 2023; ()

In this article we prove the existence of a new family of periodic solutions for discrete, nonlinear Schrodinger equations subject to spatially locali......

DISCRETIZING ADVECTION EQUATIONS WITH ROUGH VELOCITY FIELDS ON NON-CARTESIAN GRIDS

期刊: QUARTERLY OF APPLIED MATHEMATICS, 2023; ()

We investigate the properties of discretizations of advection equations on non-Cartesian grids and graphs in general. Advection equations discretized ......

MIXED DETERMINANTS, COMPENSATED INTEGRABILITY, AND NEW A PRIORI ESTIMATES IN GAS DYNAMICS

期刊: QUARTERLY OF APPLIED MATHEMATICS, 2023; 81 (2)

We extend the scope of our recent Compensated Integrability theory, by exploiting the multi-linearity of the determinant map over Symn(R). This allows......

USING BERNOULLI MAPS TO ACCELERATE MIXING OF A RANDOM WALK ON THE TORUS

期刊: QUARTERLY OF APPLIED MATHEMATICS, 2023; ()

We study the mixing time of a random walk on the torus, alternated with a Lebesgue measure preserving Bernoulli map. Without the Bernoulli map, the mi......

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