72 research outputs found
On Uniqueness of Boundary Blow-up Solutions of a Class of Nonlinear Elliptic Equations
We study boundary blow-up solutions of semilinear elliptic equations
with , or with , where is a second order
elliptic operator with measurable coefficients. Several uniqueness theorems and
an existence theorem are obtained.Comment: To appear in Comm. Partial Differential Equations; 10 page
RESQME and Stand-Alone Simulation on a Workstation
RC 16037 (#71232)
The Research Queueing Package Modeling Environment (RESQME) provides a graphical environment for constructing and solving extended queueing network models ofmanufacturing systems, for plotting graphs of results and for viewdng animations of models. The modeling environment can be run entirely on a workstation or optionally can execute large simulations on a host system using cooperative processing. In this paper we give a brief introduction to RESQME and to the RESQ modeling elements. We demonstrate how to use the package by constructing a simple model of part of a manufacturing line and solve this model to produce charts of performance measures and an animation which shows how the jobs flow through the system. By having the simulation available for use on the workstation and cooperatively on the host, RESQME provides a unique tool for understanding the performance of manufacturing systems. A user can do most of the model debugging locally on the workstation and make short pĂŒot runs to get a feeling for the amount of resources necessary to make more realistic experiments on the âą host. Then long runs which investigate large parts ofthe parameter space can be done cooperatively on the host. Whether the model is solved on the workstation or on the hosMhe graphics environment provides the same user interface to all of the underlying files. The processor where the model is solved is transparent to the user. In aU cases, the user has easy access to plots ofresults and to the animation ofthe model diagra
Supersymmetric version of a hydrodynamic system in Riemann invariants and its solutions
In this paper, a supersymmetric extension of a system of hydrodynamic type
equations involving Riemann invariants is formulated in terms of a superspace
and superfield formalism. The symmetry properties of both the classical and
supersymmetric versions of this hydrodynamical model are analyzed through the
use of group-theoretical methods applied to partial differential equations
involving both bosonic and fermionic variables. More specifically, we compute
the Lie superalgebras of both models and perform classifications of their
respective subalgebras. A systematic use of the subalgebra structures allow us
to construct several classes of invariant solutions, including travelling
waves, centered waves and solutions involving monomials, exponentials and
radicals.Comment: 30 page
Supersymmetric version of a Gaussian irrotational compressible fluid flow
The Lie point symmetries and corresponding invariant solutions are obtained
for a Gaussian, irrotational, compressible fluid flow. A supersymmetric
extension of this model is then formulated through the use of a superspace and
superfield formalism. The Lie superalgebra of this extended model is determined
and a classification of its subalgebras is performed. The method of symmetry
reduction is systematically applied in order to derive special classes of
invariant solutions of the supersymmetric model. Several new types of
algebraic, hyperbolic, multi-solitonic and doubly periodic solutions are
obtained in explicit form.Comment: Expanded introduction and added new section on classical Gaussian
fluid flow. Included several additional reference
Abstract basins of attraction
Abstract basins appear naturally in different areas of several complex
variables. In this survey we want to describe three different topics in which
they play an important role, leading to interesting open problems
Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach
Five types of blow-up patterns that can occur for the 4th-order semilinear
parabolic equation of reaction-diffusion type
u_t= -\Delta^2 u + |u|^{p-1} u \quad {in} \quad \ren \times (0,T), p>1,
\quad \lim_{t \to T^-}\sup_{x \in \ren} |u(x,t)|= +\iy, are discussed. For
the semilinear heat equation , various blow-up patterns
were under scrutiny since 1980s, while the case of higher-order diffusion was
studied much less, regardless a wide range of its application.Comment: 41 pages, 27 figure
Asymptotic behavior of solutions to the -Yamabe equation near isolated singularities
-Yamabe equations are conformally invariant equations generalizing
the classical Yamabe equation. In an earlier work YanYan Li proved that an
admissible solution with an isolated singularity at to the
-Yamabe equation is asymptotically radially symmetric. In this work
we prove that an admissible solution with an isolated singularity at to the -Yamabe equation is asymptotic to a radial
solution to the same equation on . These results
generalize earlier pioneering work in this direction on the classical Yamabe
equation by Caffarelli, Gidas, and Spruck. In extending the work of Caffarelli
et al, we formulate and prove a general asymptotic approximation result for
solutions to certain ODEs which include the case for scalar curvature and
curvature cases. An alternative proof is also provided using
analysis of the linearized operators at the radial solutions, along the lines
of approach in a work by Korevaar, Mazzeo, Pacard, and Schoen.Comment: 55 page
Definitions of quasiconformality
We establish that the infinitesimal â H -definitionâ for quasiconformal mappings on Carnot groups implies global quasisymmetry, and hence the absolute continuity on almost all lines. Our method is new even in R n where we obtain that the âlimsupâ condition in the H -definition can be replaced by a âliminfâ condition. This leads to a new removability result for (quasi)conformal mappings in Euclidean spaces. An application to parametrizations of chord-arc surfaces is also given.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46582/1/222_2005_Article_BF01241122.pd
On generation of monotonic transformations of higher order by infinitesimal transformations
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