Search results for "Boundary values"
showing 9 items of 9 documents
Zur Existenz von Lösungen gewisser Randwertaufgaben
1971
With the aid of some known results about integral equations of the Hammerstein type there is proofed an existence theorem for the following class of boundary value problems−y″−l 2 y′=f(x,y),y(a)=y(b)=0,l 2>0 mit|f(x, y)|=0,l 3 (x)>0. The existence range is determined by the greatest eigenvalue of some linear problem.
Perron's method for the porous medium equation
2016
O. Perron introduced his celebrated method for the Dirichlet problem for harmonic functions in 1923. The method produces two solution candidates for given boundary values, an upper solution and a lower solution. A central issue is then to determine when the two solutions are actually the same function. The classical result in this direction is Wiener’s resolutivity theorem: the upper and lower solutions coincide for all continuous boundary values. We discuss the resolutivity theorem and the related notions for the porous medium equation ut −∆u = 0
Boundary correspondence of Nevanlinna counting functions for self-maps of the unit disc
2003
Let ϕ \phi be a holomorphic self-map of the unit disc D \mathbb {D} . For every α ∈ ∂ D \alpha \in \partial \mathbb {D} , there is a measure τ α \tau _\alpha on ∂ D \partial \mathbb {D} (sometimes called Aleksandrov measure) defined by the Poisson representation Re ( α + ϕ ( z ) ) / ( α − ϕ ( z ) ) = ∫ P ( z , ζ ) d τ α ( ζ ) \operatorname {Re}(\alpha +\phi (z))/(\alpha -\phi (z)) = \int P(z,\zeta ) \,d\tau _\alpha (\zeta ) . Its singular part σ α \sigma _\alpha measures in a natural way the “affinity” of ϕ \phi for the boundary value α \alpha . The affinity for values w w inside D \mathbb {D} is provided by the Nevanlinna counting function N ( w ) N(w) of ϕ \phi . We introduce a natural …
Commutators, C0-semigroups and resolvent estimates
2004
Abstract We study the existence and the continuity properties of the boundary values on the real axis of the resolvent of a self-adjoint operator H in the framework of the conjugate operator method initiated by Mourre. We allow the conjugate operator A to be the generator of a C 0 -semigroup (finer estimates require A to be maximal symmetric) and we consider situations where the first commutator [ H ,i A ] is not comparable to H . The applications include the spectral theory of zero mass quantum field models.
A novel numerical meshless approach for electric potential estimation in transcranial stimulation
2015
In this paper, a first application of the method of fundamental solutions in estimating the electric potential and the spatial current density distribution in the brain due to transcranial stimulation, is presented. The coupled boundary value p roblems for the electric potential are solved in a meshless way, so avoiding the use of grid based numerical methods. A multi-spherical geometry is considered and numerical results are discussed.
Decay estimates in the supremum norm for the solutions to a nonlinear evolution equation
2014
We study the asymptotic behaviour, as t → ∞, of the solutions to the nonlinear evolution equationwhere ΔpNu = Δu + (p−2) (D2u(Du/∣Du∣)) · (Du/∣Du∣) is the normalized p-Laplace equation and p ≥ 2. We show that if u(x,t) is a viscosity solution to the above equation in a cylinder Ω × (0, ∞) with time-independent lateral boundary values, then it converges to the unique stationary solution h as t → ∞. Moreover, we provide an estimate for the decay rate of maxx∈Ω∣u(x,t) − h(x)∣.
Analytical solution for composite layered beam subjected to uniformly distributed load
2016
ABSTRACTThe article presents an analytical theory for multilayered composite beams subjected to transverse uniformly distributed loads. The formulation is based on a layerwise model characterized by third-order approximation of the axial displacements and fourth-order approximation of the transverse displacements. The layerwise kinematical model is rewritten in terms of generalized variables. The beam equilibrium equations, expressed in terms of stress resultant, allow writing the boundary value governing problem. The layerwise fields are obtained by postprocessing steps. The main advantage is to ensure the accuracy level associated to the layerwise formulations preserving the computational…
Ordinary (p1,…,pm)-Laplacian systems with mixed boundary value conditions
2016
Abstract In this paper we prove the existence of multiple weak solutions for an ordinary mixed boundary value system with ( p 1 , … , p m )-Laplacian by using recent results of critical points.
Infinitely many weak solutions for a mixed boundary value system with (p_1,…,p_m)-Laplacian
2014
The aim of this paper is to prove the existence of infinitely many weak solu- tions for a mixed boundary value system with (p1, . . . , pm)-Laplacian. The approach is based on variational methods.