Search results for "Boundary value problem"
showing 10 items of 551 documents
On the finite element approximation for maxwell’s problem in polynomial domains of the plane
1981
The time-harmonic Maxwell boundary value problem in polygonal domains of R2 is considered. The behaviour of the solution in the neighbourhood of nonregular boundary points is given and asymptotic error estimates in L2- and in curl-div-norm for a finite element approximation of the solution are derived
AN HYPERBOLIC-PARABOLIC PREDATOR-PREY MODEL INVOLVING A VOLE POPULATION STRUCTURED IN AGE
2020
Abstract We prove existence and stability of entropy solutions for a predator-prey system consisting of an hyperbolic equation for predators and a parabolic-hyperbolic equation for preys. The preys' equation, which represents the evolution of a population of voles as in [2] , depends on time, t, age, a, and on a 2-dimensional space variable x, and it is supplemented by a nonlocal boundary condition at a = 0 . The drift term in the predators' equation depends nonlocally on the density of preys and the two equations are also coupled via classical source terms of Lotka-Volterra type, as in [4] . We establish existence of solutions by applying the vanishing viscosity method, and we prove stabil…
Full Sliding “Adhesive-Like” Contact of V-Belts
2002
Abstract Analysis of power transmission in a belt drive consisting of e. g. two pulleys might be treated as a boundary value problem. Tight side tension FT, slack side tension FS and the wrap angle α are the three natural boundary conditions. In the literature, theories are developed where seating and unseating as well as the power transmitting part of the contact are considered. The solutions presented so far don’t fulfil the boundary conditions properly, since a certain tension ratio FT/FS is associated with a certain contact angle and not an a priori specified one. It appears that a new type of full sliding solution must be introduced to handle the boundary condition problem. During part…
Fizikas un matemātikas zinātņu doktors Arnolds Lepins: biobibliogrāfiskais rādītājs
1990
Biobibliogrāfiskajā rādītājā ietverti fizikas un matemātikas zinātņu doktora profesora Arnolda Lepina publicētie darbi no 1952.gada līdz 1991.gadam, kā ari uzrādīta literatūra par viņu.
Ab initio study of the F centers in CaF2: Calculations of the optical absorption, diffusion and binding energies
1998
Abstract The ground electronic state of the F center in CaF 2 crystal, its optical absorption energy, the activation energy of thermal diffusion and M center dissociation to pair of F centers are calculated using the Hartree-Fock embedded molecular cluster method. Different pseudopotentials, basis sets, boundary conditions and two computer codes, EMBED96 and Gaussian94, are employed and their results compared.
A note on homoclinic solutions of (p,q)-Laplacian difference equations
2019
We prove the existence of at least two positive homoclinic solutions for a discrete boundary value problem of equations driven by the (p,q) -Laplace operator. The properties of the nonlinearity ensure that the energy functional, corresponding to the problem, satisfies a mountain pass geometry and a Palais–Smale compactness condition.
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.
Multiplicity of solutions to a nonlinear boundary value problem of concave–convex type
2015
Abstract Problem (P) { − Δ p u + | u | p − 2 u = | u | r − 1 u x ∈ Ω | ∇ u | p − 2 ∂ u ∂ ν = λ | u | s − 1 u x ∈ ∂ Ω , where Ω ⊂ R N is a bounded smooth domain, ν is the unit outward normal at ∂ Ω , Δ p is the p -Laplacian operator and λ > 0 is a parameter, was studied in Sabina de Lis (2011) and Sabina de Lis and Segura de Leon (in press). Among other features, it was shown there that when exponents lie in the regime 1 s p r , a minimal positive solution exists if 0 λ ≤ Λ , for a certain finite Λ , while no positive solutions exist in the complementary range λ > Λ . Furthermore, in the radially symmetric case a second positive solution exists for λ varying in the same full range ( 0 , Λ ) …
A priori bounds and multiplicity of solutions for an indefinite elliptic problem with critical growth in the gradient
2019
Let $\Omega \subset \mathbb R^N$, $N \geq 2$, be a smooth bounded domain. We consider a boundary value problem of the form $$-\Delta u = c_{\lambda}(x) u + \mu(x) |\nabla u|^2 + h(x), \quad u \in H^1_0(\Omega)\cap L^{\infty}(\Omega)$$ where $c_{\lambda}$ depends on a parameter $\lambda \in \mathbb R$, the coefficients $c_{\lambda}$ and $h$ belong to $L^q(\Omega)$ with $q>N/2$ and $\mu \in L^{\infty}(\Omega)$. Under suitable assumptions, but without imposing a sign condition on any of these coefficients, we obtain an a priori upper bound on the solutions. Our proof relies on a new boundary weak Harnack inequality. This inequality, which is of independent interest, is established in the gener…
\( L^{1} \) existence and uniqueness results for quasi-linear elliptic equations with nonlinear boundary conditions
2007
Abstract In this paper we study the questions of existence and uniqueness of weak and entropy solutions for equations of type − div a ( x , D u ) + γ ( u ) ∋ ϕ , posed in an open bounded subset Ω of R N , with nonlinear boundary conditions of the form a ( x , D u ) ⋅ η + β ( u ) ∋ ψ . The nonlinear elliptic operator div a ( x , D u ) is modeled on the p-Laplacian operator Δ p ( u ) = div ( | D u | p − 2 D u ) , with p > 1 , γ and β are maximal monotone graphs in R 2 such that 0 ∈ γ ( 0 ) and 0 ∈ β ( 0 ) , and the data ϕ ∈ L 1 ( Ω ) and ψ ∈ L 1 ( ∂ Ω ) .