First eigenvalue of one-dimensional diffusion processes.

Wang, Jian

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Displaying similar documents to “First eigenvalue of one-dimensional diffusion processes.”

Destabilization for quasivariational inequalities of reaction-diffusion type

Vítězslav Babický (2000)

Applications of Mathematics

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We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.

Arnold diffusion: a variational construction.

Xia, Zhihong (1998)

Documenta Mathematica

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Principle of superposition and interference of diffusion processes

Masao Nagasawa (1993)

Séminaire de probabilités de Strasbourg

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Homogenization of the transport equation describing convection-diffusion processes in a material with fine periodic structure

Šilhánek, David, Beneš, Michal

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In the present contribution we discuss mathematical homogenization and numerical solution of the elliptic problem describing convection-diffusion processes in a material with fine periodic structure. Transport processes such as heat conduction or transport of contaminants through porous media are typically associated with convection-diffusion equations. It is well known that the application of the classical Galerkin finite element method is inappropriate in this case since the discrete...

Guaranteed two-sided bounds on all eigenvalues of preconditioned diffusion and elasticity problems solved by the finite element method

Martin Ladecký, Ivana Pultarová, Jan Zeman (2021)

Applications of Mathematics

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A method of characterizing all eigenvalues of a preconditioned discretized scalar diffusion operator with Dirichlet boundary conditions has been recently introduced in Gergelits, Mardal, Nielsen, and Strakoš (2019). Motivated by this paper, we offer a slightly different approach that extends the previous results in some directions. Namely, we provide bounds on all increasingly ordered eigenvalues of a general diffusion or elasticity operator with tensor data, discretized with the conforming...

Diffusion and cross-diffusion in pattern formation

Wei-Ming Ni (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We discuss the stability and instability properties of steady state solutions to single equations, shadow systems, as well as $2 \times 2$ systems. Our basic observation is that the more complicated the pattern are, the more unstable they tend to be.

Behaviour of global solutions for a system of reaction-diffusion equations from combustion theory

Salah Badraoui (1999)

Applicationes Mathematicae

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We are concerned with the boundedness and large time behaviour of the solution for a system of reaction-diffusion equations modelling complex consecutive reactions on a bounded domain under homogeneous Neumann boundary conditions. Using the techniques of E. Conway, D. Hoff and J. Smoller [3] we also show that the bounded solution converges to a constant function as t → ∞. Finally, we investigate the rate of this convergence.