The initial-value problem is studied for evolution equations in Hilbert space of the general form d/dt A(u) + B(u) ϶ f, where and are maximal monotone operators. Existence of a solution is proved when A is a subgradient and either is strongly monotone or B is coercive; existence is established...
A mixed initial and boundary value problem is considered for
a partial differential equation of the form Muₜ(x, t)+Lu(x, t)=0,
where M and L are elliptic differential operators of orders 2 m
and 2l, respectively, with m ≤ l. The existence and uniqueness
of a strong solution of this equation...
Advective skew dispersion is a natural Markov process defined ned
by a di ffusion with drift across an interface of jump discontinuity in
a piecewise constant diff usion coeffcient. In the absence of drift this
process may be represented as a function of -skew Brownian motion
for a uniquely determined...
We consider solutions to the two-dimensional incompressible Navier-Stokes and Euler equations for which velocity and vorticity are bounded in the plane. We show that for every T > 0, the Navier-Stokes velocity converges in L∞([0,T]; L∞(R²)) as viscosity approaches 0 to the Euler velocity generated from the same initial data....
This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with formulations in terms of partial differential equations governing the conservative, advective-dispersive transport of mass concentrations in divergence form,...
Average annual losses caused by geologic hazards in Oregon are difficult to determine, owing to incomplete and scattered data. Preliminary considerations, however, indicate that losses to landslides may total between $4 million and $40 million per year. As many as nine persons have been killed by one landslide in Oregon...
We consider flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are treated with Neumann type flow conditions, and a novel treatment of the so called Kutta-Joukowsky flow conditions are given in the subsonic case. The...
The purpose of this note is to provide a coupling of weak limits in distribution of sequence of (normalized) multiplicative cascade measures under strong disorder in terms of the extremes of an associated branching random walk, assuming i.i.d positive, non-lattice bond weights and a second moment condition. The solution is...
The convolution inequality h ∗ h(ξ) ≤ B|ξ|θh(ξ) defined on Rⁿ
arises from a probabilistic representation of solutions of the n-dimensional
Navier-Stokes equations, n ≥ 2. Using a chaining argument, we establish
in all dimensions n ≥ 1 the nonexistence of strictly positive fully supported
solutions of this inequality for...
In this paper we extend the results of the research started by the first author in which Karlin-McGregor diagonalization of certain reversible Markov chains over countably infinite general state spaces by orthogonal polynomials was used to estimate the rate of convergence to a stationary distribution. We use a method of...
A mathematical model of a differential thermal analysis (DTA)
system was formulated so that influence of the various physical parameters
on the DTA peak could be determined. The specific DTA apparatus
simulated had cylindrical sample holes drilled into a nickel
block considered to have a negligible thermal resistance, and the...
The surgery technique of Gromov and Lawson may be used to construct families of positive scalar curvature metrics which are parameterised by Morse functions. This has played an important role in the study of the space of metrics of positive scalar curvature on a smooth manifold and its corresponding moduli...
For each Cantor set C in R³, all points of which have bounded local genus, we show that there are infinitely many inequivalent Cantor sets in R³ with the complement having the same fundamental group as the complement of C. This answers a question from Open Problems in Topology and...
Given two rational maps φ and ψ on Ρ¹ of degree at least two, we study a symmetric, nonnegative real-valued pairing〈φ, ψ〉which is closely related to the canonical height functions hφ and hψ associated to these maps. Our main results show a strong connection between the value of〈φ, ψ〉and the...
Extensions of the fractional Brownian fields are constructed over
a complete Riemannian manifold. This construction is carried out for the full
range of the Hurst parameter α ∈ (0, 1). In particular, we establish existence,
distributional scaling (self-similiarity), stationarity of the increments, and almost
sure H¨older continuity of sample paths....
Let X and Y be a pair of smooth manifolds, each obtainable
from the other by surgery in codimension at least three. We show that the
corresponding spaces Riem⁺(X) and Riem⁺(Y), respectively consisting of
Riemannian metrics of positive scalar curvature on X and Y, are homotopy
equivalent. This result is...
For every finitely generated abelian group G, we construct an irreducible
open 3-manifold M[subscript G] whose end set is homeomorphic to a Cantor set and
whose homogeneity group is isomorphic to G. The end homogeneity group
is the group of self-homeomorphisms of the end set that extend to homeomorphisms
of...