# DOMAIN DECOMPOSITION METHODS WITH OVERLAPPING SUBDOMAINS FOR THE TIME-DEPENDENT PROBLEMS OF MATHEMATICAL PHYSICS

## Related Articles

- Behavior of solutions to elliptic boundary value problems in a neighborhood of corner points of discontinuity lines of the coefficients. Bogolyubov, A.; Mogilevskii, I. // Computational Mathematics & Mathematical Physics;Dec2011, Vol. 51 Issue 12, p2121
A representation of the solution to an elliptic boundary value problem in the vicinity of a corner point on the discontinuity line of the coefficient of the higher order derivative is constructed. The study is based on the method of additive separation of singularities proposed by Kondrat'ev.

- The method of fundamental solutions for a biharmonic inverse boundary determination problem. Zeb, A.; Ingham, D. B.; Lesnic, D. // Computational Mechanics;Sep2008, Vol. 42 Issue 3, p371
In this paper, a nonlinear inverse boundary value problem associated to the biharmonic equation is investigated. This problem consists of determining an unknown boundary portion of a solution domain by using additional data on the remaining known part of the boundary. The method of fundamental...

- Estimates for the Approximation Numbers of One Class of Integral Operators. I. Lomakina, E. N. // Siberian Mathematical Journal;Jan/Feb2003, Vol. 44 Issue 1, p147
Unlike the familiar problems for mixed-type equations, we pose a boundary value problem for the Lavrent'ev-Bitsadze equation in domains with unbounded multiply connected hyperbolicity subdomains. We prove unique solvability in explicit form. We also study this problem for the general...

- Optimization of a Direct Elliptic Boundary Value Problem Solver by the Combined Use of Symmetry and Strassen's Algorithm. Qaddouri, Abdessamad; Còté, Jean // Monthly Weather Review;Nov2004, Vol. 132 Issue 11, p2708
A direct elliptic boundary value problem solver used for meteorological applications has been optimized. The problem to be solved is symmetric under a parity operation, and this is preserved by discretization. Therefore if the mesh possesses this symmetry, then the discretized problem will share...

- Integral representations and boundary value problems for a second-order elliptic system with a singular point. Rasulov, A. // Differential Equations;Feb2010, Vol. 46 Issue 2, p277
For a second-order elliptic system with a singular point, we obtain integral representations and inversion formulas for the case in which the singular point is an interior point of the domain. In the integral representations, we clearly extract the singular part of the solutions, which permits...

- Boundary-value Problems with Non-Local Initial Condition for Parabolic Equations with Parameter. Rassias, John Michael; Karimov, Erkinjon Tulkinovich // European Journal of Pure & Applied Mathematics;2010, Vol. 3 Issue 6, p948
In 2002, J.M.Rassias (Uniqueness of quasi-regular solutions for bi-parabolic elliptic bi-hyperbolic Tricomi problem, Complex Variables, 47 (8) (2002), 707-718) imposed and investigated the bi-parabolic elliptic bi-hyperbolic mixed type partial differential equation of second order. In the...

- Multiple Solutions for a Fourthâ€“order Asymptotically Linear Elliptic Problem. Ai Qian; Shu Li // Acta Mathematica Sinica;Jul2006, Vol. 22 Issue 4, p1121
Under simple conditions, we prove the existence of three solutions for a fourthâ€“order asymptotically linear elliptic boundary value problem. For the resonance case at infinity, we do not need to assume any more conditions to ensure the boundedness of the (PS) sequence of the corresponding...

- Multiple Positive Solutions via Index Theory for Singular Boundary Value Problems with Derivative Dependence. Baoqiang Yan; Donal OâRegan; Ravi Agarwal // Positivity;Nov2007, Vol. 11 Issue 4, p687
AbstractÃ‚Â Ã‚Â The existence of multiple positive solutions is presented for the singular second-order boundary value problems $$\left\{\begin{array}{ll} x^{\prime\prime}\Phi(t)f(t,x,x') =0, 0 using the fixed point index, where f may be singular at x Ã‚Â =Ã‚Â 0 and...

- On Systems of Boundary Value Problems for Differential Inclusions. Erbe, Lynn; Tisdell, Christopher C.; Wong, Patricia J. Y. // Acta Mathematica Sinica;Mar2007, Vol. 23 Issue 3, p549
Herein we consider the existence of solutions to second-order, two-point boundary value problems (BVPs) for systems of ordinary differential inclusions. Some new Bernsteinâ€“Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential...