Search results for "robin boundary condition"
showing 10 items of 24 documents
Boundary discretization based on the residual energy using the SGBEM
2007
Abstract The paper has as objective the estimation of the error in the structural analysis performed by using the displacement approach of the Symmetric Galerkin Boundary Element Method (SGBEM) and suggests a strategy able to reduce this error through an appropriate change of the boundary discretization. The body, characterized by a domain Ω and a boundary Γ−, is embedded inside a complementary unlimited domain Ω∞⧹Ω bounded by a boundary Γ+. In such new condition it is possible to perform a separate valuation of the strain energies in the two subdomains through the computation of the work, defined generalized, obtained as the product among nodal and weighted quantities on the actual boundar…
On the Prandtl Boundary Layer Equations in Presence of Corner Singularities
2014
In this paper we prove the well-posedness of the Prandtl boundary layer equations on a periodic strip when the initial and the boundary data are not assigned to be compatible.
Pairs of solutions for Robin problems with an indefinite and unbounded potential, resonant at zero and infinity
2018
We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential and a Caratheodory reaction term which is resonant both at zero and $$\pm \infty $$ . Using the Lyapunov–Schmidt reduction method and critical groups (Morse theory), we show that the problem has at least two nontrivial smooth solutions.
Robin problems with general potential and double resonance
2017
Abstract We consider a semilinear elliptic problem with Robin boundary condition and an indefinite and unbounded potential. The reaction term is a Caratheodory function exhibiting linear growth near ± ∞ . We assume that double resonance occurs with respect to any positive spectral interval. Using variational tools and critical groups, we show that the problem has a nontrivial smooth solution.
Superlinear Robin Problems with Indefinite Linear Part
2018
We consider a semilinear Robin problem with an indefinite linear part and a superlinear reaction term, which does not satisfy the usual in such cases AR condition. Using variational methods, together with truncation–perturbation techniques and Morse theory (critical groups), we establish the existence of three nontrivial solutions. Our result extends in different ways the multiplicity theorem of Wang.
Two-Sided Estimates of the Solution Set for the Reaction–Diffusion Problem with Uncertain Data
2009
We consider linear reaction–diffusion problems with mixed Dirichlet–Neumann–Robin conditions. The diffusion matrix, reaction coefficient, and the coefficient in the Robin boundary condition are defined with an uncertainty which allow bounded variations around some given mean values. A solution to such a problem cannot be exactly determined (it is a function in the set of “possible solutions” formed by generalized solutions related to possible data). The problem is to find parameters of this set. In this paper, we show that computable lower and upper bounds of the diameter (or radius) of the set can be expressed throughout problem data and parameters that regulate the indeterminacy range. Ou…
Strictly convergent algorithm for an elliptic equation with nonlocal and nonlinear boundary conditions
2012
The paper describes a formally strictly convergent algorithm for solving a class of elliptic problems with nonlinear and nonlocal boundary conditions, which arise in modeling of the steady-state conductive-radiative heat transfer processes. The proposed algorithm has two levels of iterations, where inner iterations by means of the damped Newton method solve an appropriate elliptic problem with nonlinear, but local boundary conditions, and outer iterations deal with nonlocal terms in boundary conditions.
Optimal control in models with conductive‐radiative heat transfer
2003
In this paper an optimal control problem for the elliptic boundary value problem with nonlocal boundary conditions is considered. It is shown that the weak solutions of the boundary value problem depend smoothly on the control parameter and that the cost functional of the optimal control problem is Frechet differentiable with respect to the control parameter. Optimalus valdymas modeliuose su laidžiu-radioaktyviu šilumos pernešimu Santrauka Darbe nagrinejamas nelokalaus kraštinio uždavinio optimalaus valdymo uždavinys. Parodyta, kad silpnasis kraštinio uždavinio sprendinys tolydžiai priklauso nuo valdomojo parametro, taigi, optimalaus valdymo tikslo funkcija yra diferencijuojama Freše prasme…
Boundary value problem with integral condition for a Blasius type equation
2016
The steady motion in the boundary layer along a thin flat plate, which is immersed at zero incidence in a uniform stream with constant velocity, can be described in terms of the solution of the differential equation x'''= -xx'', which satisfies the boundary conditions x(0) = x'(0) = 0, x'(∞) = 1. The author investigates the generalized boundary value problem consisting of the nonlinear third-order differential equation x''' = -trx|x|q-1x'' subject to the integral boundary conditions x(0) = x'(0) = 0, x'(∞) = λ∫0ξx(s) ds, where 0 0 is a parameter. Results on the existence and uniqueness of solutions to boundary value problem are established. An illustrative example is provided.
On a Robin (p,q)-equation with a logistic reaction
2019
We consider a nonlinear nonhomogeneous Robin equation driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation) plus an indefinite potential term and a parametric reaction of logistic type (superdiffusive case). We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter \(\lambda \gt 0\) varies. Also, we show that for every admissible parameter \(\lambda \gt 0\), the problem admits a smallest positive solution.