Search results for "partial differential equation"
showing 10 items of 326 documents
Quasihyperbolic boundary conditions and capacity: Uniform continuity of quasiconformal mappings
2005
We prove that quasiconformal maps onto domains which satisfy a suitable growth condition on the quasihyperbolic metric are uniformly continuous when the source domain is equipped with the internal metric. The obtained modulus of continuity and the growth assumption on the quasihyperbolic metric are shown to be essentially sharp. As a tool, we prove a new capacity estimate.
Solutions to the 1-harmonic flow with values into a hyper-octant of the N-sphere
2013
Abstract We announce existence results for the 1-harmonic flow from a domain of R m into the first hyper-octant of the N -dimensional unit sphere, under homogeneous Neumann boundary conditions. The arguments rely on a notion of “geodesic representative” of a BV-vector field on its jump set.
THE 1-HARMONIC FLOW WITH VALUES IN A HYPEROCTANT OF THE N-SPHERE
2014
We prove the existence of solutions to the 1-harmonic flow — that is, the formal gradient flow of the total variation of a vector field with respect to the [math] -distance — from a domain of [math] into a hyperoctant of the [math] -dimensional unit sphere, [math] , under homogeneous Neumann boundary conditions. In particular, we characterize the lower-order term appearing in the Euler–Lagrange formulation in terms of the “geodesic representative” of a BV-director field on its jump set. Such characterization relies on a lower semicontinuity argument which leads to a nontrivial and nonconvex minimization problem: to find a shortest path between two points on [math] with respect to a metric w…
Fractional-order theory of thermoelasticicty. I: Generalization of the Fourier equation
2018
The paper deals with the generalization of Fourier-type relations in the context of fractional-order calculus. The instantaneous temperature-flux equation of the Fourier-type diffusion is generalized, introducing a self-similar, fractal-type mass clustering at the micro scale. In this setting, the resulting conduction equation at the macro scale yields a Caputo's fractional derivative with order [0,1] of temperature gradient that generalizes the Fourier conduction equation. The order of the fractional-derivative has been related to the fractal assembly of the microstructure and some preliminary observations about the thermodynamical restrictions of the coefficients and the state functions r…
Approximate analytic and numerical solutions to Lane-Emden equation via fuzzy modeling method
2012
Published version in the journal: Mathematical Problems in Engineering. Also available from the publisher: http://dx.doi.org/10.1155/2012/259494 A novel algorithm, called variable weight fuzzy marginal linearization VWFML method, is proposed. Thismethod can supply approximate analytic and numerical solutions to Lane-Emden equations. And it is easy to be implemented and extended for solving other nonlinear differential equations. Numerical examples are included to demonstrate the validity and applicability of the developed technique.
Holder continuity of solutions for a class of nonlinear elliptic variational inequalities of high order
2001
Propagation of plane and cylindrical waves in turbulent superfluid helium
2014
In this paper, the equations that govern the propagation of plane and cylindrical waves in turbulent superfluid solutions in some simplified cases are determined.
Cross-Diffusion Driven Instability in a Predator-Prey System with Cross-Diffusion
2013
In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing mechanism that leads to the emergence of spatial patterns. Near marginal stability we perform a weakly nonlinear analysis to predict the amplitude and the form of the pattern, deriving the Stuart-Landau amplitude equations. Moreover, in a large portion of the subcritical zone, numerical simulations show the emergence of oscillating patterns, which cannot be predicted by the weakly nonlinear analysis. Finally when the pattern invades the domain as a trave…
Rotationally symmetric 1-harmonic flows from D2 TO S 2: Local well-posedness and finite time blowup
2010
The 1-harmonic flow from the disk to the sphere with constant Dirichlet boundary conditions is analyzed in the case of rotational symmetry. Sufficient conditions on the initial datum are given, such that a unique classical solution exists for short times. Also, a sharp criterion on the boundary condition is identified, such that any classical solution will blow up in finite time. Finally, nongeneric examples of finite time blowup are exhibited for any boundary condition.
Some Theoretical Results About Stability for IMEX Schemes Applied to Hyperbolic Equations with Stiff Reaction Terms
2010
In this work we are concerned with certain numerical difficulties associated to the use of high order Implicit–Explicit Runge–Kutta (IMEX-RK) schemes in a direct discretization of balance laws with stiff source terms. We consider a simple model problem, introduced by LeVeque and Yee in [J. Comput. Phys 86 (1990)], as the basic test case to explore the ability of IMEX-RK schemes to produce and maintain non-oscillatory reaction fronts.