Search results for "Compact"
showing 10 items of 531 documents
Random attractors for stochastic lattice systems with non-Lipschitz nonlinearity
2011
In this article, we study the asymptotic behaviour of solutions of a first-order stochastic lattice dynamical system with an additive noise. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions so that uniqueness of the Cauchy problem fails to be true. Using the theory of multi-valued random dynamical systems, we prove the existence of a random compact global attractor.
Homoclinic Solutions of Nonlinear Laplacian Difference Equations Without Ambrosetti-Rabinowitz Condition
2021
The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using Ambrosetti-Rabinowitz type-conditions. The main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals.
Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation
2004
A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.
Lacunary bifurcation for operator equations and nonlinear boundary value problems on ℝN
1991
SynopsisWe consider nonlinear eigenvalue problems of the form Lu + F(u) = λu in a real Hilbert space, where L is a positive self-adjoint linear operator and F is a nonlinearity vanishing to higher order at u = 0. We suppose that there are gaps in the essential spectrum of L and use critical point theory for strongly indefinite functionals to derive conditions for the existence of non-zero solutions for λ belonging to such a gap, and for the bifurcation of such solutions from the line of trivial solutions at the boundary points of a gap. The abstract results are applied to the L2-theory of semilinear elliptic partial differential equations on ℝN. We obtain existence results for the general c…
Morphological determination of the phototrophic community composition of biological soil crusts in coastal sand dunes in northern Germany
2022
This dataset comprises the microbial community composition of biological soil crusts in north-German sand dunes. For this we obtained enrichment cultures of phototrophic microorganisms, by placing fragments of biocrusts of the same Petri dishes as used for sequencing, in Petri dishes with Bold Basal (1N BBM) agarized medium (Bischoff and Bold 1963). Cultures were grown under standard laboratory conditions: with a 12-hour alteration of light and dark phases and irradiation of 25 μmol photons m-2 s-1 at a temperature 20 ± 5 ºС. Microscopic study of these raw cultures began in the third week of cultivation. Morphological examinations were performed using Olympus BX53 light microscope with Noma…
Some results about operators in nested Hilbert spaces
2005
With the use of interpolation methods we obtain some results about the domain of an operator acting on the nested Hilbert space {ℋf}f∈∑ generated by a self-adjoint operatorA and some estimates of the norms of its representatives. Some consequences in the particular case of the scale of Hilbert spaces are discussed.
Existence for shape optimization problems in arbitrary dimension
2002
We discuss some existence results for optimal design problems governed by second order elliptic equations with the homogeneous Neumann boundary conditions or with the interior transmission conditions. We show that our continuity hypotheses for the unknown boundaries yield the compactness of the associated characteristic functions, which, in turn, guarantees convergence of any minimizing sequences for the first problem. In the second case, weaker assumptions of measurability type are shown to be sufficient for the existence of the optimal material distribution. We impose no restriction on the dimension of the underlying Euclidean space.
Morphological characterisation of soil structure in tilled fields: from a diagnosis method to the modelling of structural changes over time
2004
Characterisation of soit structure within the tilled layer of cultivated fields is crucial because the importance of this soil characteristic on the biological, chemical and physical properties of the soil and its repercussions on water cycle, root growth and functioning. We present in this paper a method for field characterisation of soil structure. This method, practised since the 1970s, was designed for field diagnosis of the effects of cropping systems on soil structure. It is based on a stratification of the observation face of a pit dug perpendicular to the direction of tillage and traffic: spatial compartments are distinguished, according to the nature of the mechanical stresses they…
Resource or waste? A perspective of plastics degradation in soil with a focus on end-of-life options.
2018
‘Capable-of-being-shaped’ synthetic compounds are prevailing today over horn, bone, leather, wood, stone, metal, glass, or ceramic in products that were previously left to natural materials. Plastic is, in fact, economical, simple, adaptable, and waterproof. Also, it is durable and resilient to natural degradation (although microbial species capable of degrading plastics do exist). In becoming a waste, plastic accumulation adversely affects ecosystems. The majority of plastic debris pollutes waters, accumulating in oceans. And, the behaviour and the quantity of plastic, which has become waste, are rather well documented in the water, in fact. This review collects existing information on pla…
A PDE model for the spatial dynamics of a voles population structured in age
2020
Abstract We prove existence and stability of entropy weak solutions for a macroscopic PDE model for the spatial dynamics of a population of voles structured in age. The model consists of a scalar PDE depending on time, t , age, a , and space x = ( x 1 , x 2 ) , supplemented with a non-local boundary condition at a = 0 . The flux is linear with constant coefficient in the age direction but contains a non-local term in the space directions. Also, the equation contains a term of second order in the space variables only. Existence of solutions is established by compensated compactness, see Panov (2009), and we prove stability by a doubling of variables type argument.