International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 11, Page 687-694, 2002., 2002 We solve the Dirichlet problem for acoustic scattering from a surface which has been perturbed by the addition of one or more bumps. We build the solution for the bumpy case using the Green′s function for the unperturbed surface, and the solution of a local integral equation in which the integration is carried out only over the added bumps. We conclude
Maxim J. Goldberg, Seonja Kim
wiley +1 more source
Diffusion and propagation problems in some ramified domains with a fractal boundary [PDF]
, 2006 This paper is devoted to some elliptic boundary value problems in a self-similar ramified domain of R 2 with a fractal boundary. Both the Laplace and Helmholtz equations are studied.
Yves Achdou +5 more
core +1 more source
On some classes of generalized Schrödinger equations
Advances in Nonlinear Analysis, 2020 Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + ∑i=2m$\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved
Correa Leão Amanda S. S. +3 more
doaj +1 more source
On Principle Eigenvalue for Linear Second Order Elliptic Equations in Divergence Form [PDF]
, 2003 2002 Mathematics Subject Classification: 35J15, 35J25, 35B05, 35B50The principle eigenvalue and the maximum principle for second-order elliptic equations is studied.
Fabricant, A., Kutev, N., Rangelov, T.
core
On the logarithm of the minimizing integrand for certain variational problems in two dimensions [PDF]
, 2020 Let be a smooth convex homogeneous function of degree , 1 < < ∞, on ℂ ∖ {0}. We show that if is a minimizer for the functional whose integrand is (∇ ), in a certain subclass of the Sobolev space 1, (Ω), and ∇ ∕ = 0 at ∈ Ω, then in a neighborhood of
Andrew Vogel, John L Lewis, Murat Akman
core
Многомерни операционни смятания за нелокални гранични задачи за еволюционни уравнения [PDF]
, 2011 [Dimovski Ivan H.; Димовски Иван Х.]; [Tsankov Yulian Ts.; Цанков Юлиан Ц.]Here we propose a direct operational calculus approach to nonlocal boundary value problems for a large class of linear evolution equations with several space variables and one ...
Dimovski, Ivan H., Tsankov, Yulian Ts.
core
Advanced Nonlinear Studies, 2018 This paper is concerned with the boundary behavior of the unique convex solution to a singular Dirichlet problem for the Monge–Ampère ...
Zhang Zhijun
doaj +1 more source
Elliptic equations in divergence form, geometric critical points of solutions and Stekloff eigenfunctions [PDF]
, 1994 . The Stekloff eigenvalue problem (1.1) has a ’ countable number of eigenvalues (Pn}n = 1,2..... each of finite multiplicity. In this paper the authors give an upper estimate, in terms of the integer n, of the multiplicity of Pn, and the number of ...
ALESSANDRINI, GIOVANNI +4 more
core +1 more source
Existence, multiplicity and nonexistence results for Kirchhoff type equations
Advances in Nonlinear Analysis, 2020 In this paper, we study following Kirchhoff type equation:
He Wei, Qin Dongdong, Wu Qingfang
doaj +1 more source
ESAIM: Mathematical Modelling and Numerical Analysis SMALL AMPLITUDE HOMOGENIZATION APPLIED TO MODELS OF NON-PERIODIC FIBROUS MATERIALS [PDF]
, 2007 . In this paper, we compare a biomechanics empirical model of the heart fibrous structure to two models obtained by a non-periodic homogenization process.
David Manceau
core