Results 1 to 10 of about 5,044 (169)

On the Solution of the Dirichlet Problem for Second-Order Elliptic Systems in the Unit Disk

Mathematics, 2023
The role played by explicit formulas for solving boundary value problems for elliptic equations and systems is well known. In this paper, explicit formulas for a general solution of the Dirichlet problem for second-order elliptic systems in the unit disk
Astamur Bagapsh, Alexandre Soldatov
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On the generalized spectrum for second-order elliptic systems [PDF]

Transactions of the American Mathematical Society, 1987
We consider the system of homogeneous Dirichlet boundary value problems ( ∗
Cantrell, Robert Stephen, Cosner, Chris
openaire   +1 more source

A Comparison of Parallel Algorithms for Numerical Solution of Parabolic Problems with Fractional Power Elliptic Operators

Axioms, 2022
In this article we construct parallel solvers analyze the efficiency and accuracy of general parallel solvers for three dimensional parabolic problems with the fractional power of elliptic operators.
Raimondas Čiegis, Ignas Dapšys, Remigijus Čiegis   +2 more
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High-precision quantum algorithms for partial differential equations [PDF]

Quantum, 2021
Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description.
Andrew M. Childs, Jin-Peng Liu, Aaron Ostrander   +2 more
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The explicit solution of the Neumann boundary value problem for Bauer differential equation in circular domains [PDF]

Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2021
The article is devoted to the boundary value problem of Neumann problem's type for solutions of one second-order elliptic differential equation.
Rasulov, Karim Magomedovich, Nagornaya, Tatiana Романовна   +1 more
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Uniqueness theorem for partially observed elliptic systems and application to asymptotic synchronization

Comptes Rendus. Mathématique, 2020
We show that under Kalman’s rank condition, the observability of a scalar equation implies the uniqueness of solution to a system of elliptic operators.
Li, Tatsien, Rao, Bopeng
doaj   +1 more source

The p-ellipticity condition for second order elliptic systems and applications to the Lamé and homogenization problems

Journal of Differential Equations, 2021
The notion of $p$-ellipticity has recently played a significant role in improving our understanding of issues of solvability of boundary value problems for scalar complex valued elliptic PDEs. In particular, the presence of $p$-ellipticity ensures higher regularity of solutions of such equations.
Martin Dindoš, Jungang Li, Jill Pipher
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On nonnegative radial entire solutions of second order quasilinear elliptic systems

Electronic Journal of Qualitative Theory of Differential Equations, 2002
In this article we consider the second order quasilinear elliptic system of the form $$\Delta_{p_i} u_i=H_i(|x|)u_{i+1}^{\alpha_i}, x\in \mathbb{R}^N, i=1,2,...,m$$ with nonnegative continuous function $H_i$.
T. Teramoto
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NONTRIVIAL RADIAL SOLUTIONS FOR A SYSTEM OF SECOND ORDER ELLIPTIC EQUATIONS

Journal of Applied Analysis & Computation, 2022
Summary: In this paper we use the topological degree and the Krein-Rutman theorem to investigate the existence of nontrivial radial solutions for a system of second order elliptic equations. Our results are obtained under some conditions involving the eigenvalues of a relevant linear operator.
Zhang, Haiyan, Xu, Jiafa, O'Regan, Donal
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On energy functionals for second order elliptic systems with constant coefficients

Ufa Mathematical Journal, 2022
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Astamur Olegovich Bagapsh, Konstantin Yurievich Fedorovskiy   +1 more
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