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...