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Study of ODE limit problems for reaction-diffusion equations

Simsen J., Simsen M. S., Zimmermann A.

Opuscula Mathematica

2018

Vol. 38, no. 1

117--131

In this work we study ODE limit problems for reaction-diffusion equations for large diffusion and we study the sensitivity of nonlinear ODEs with respect to initial conditions and exponent parameters. Moreover, we prove continuity of the flow and weak upper semicontinuity of a family of global attractors for reaction-diffusion equations with spatially variable exponents when the exponents go to 2 in [formula] and the diffusion coefficients go to infinity.

Interior controllability of the Benjamin-Bona-Mahony equation

Leiva H., Merentes N., Sanchez J.

Journal of Mathematics and Applications

2010

Vol. 33

51-59

In this paper we prove the interior approximate controllability of the following Generalized Benjamin-Bona-Mahony type equation (BBM) with homogeneous Dirichlet boundary conditions [formula/wzór] where a(mniejszy-równy) and b > 0 are constants, Ω is a domain in IR(N), ω is an open nonempty subset of Ω denotes the characteristic function of the set ω and the distributed control [formula/wzór]. We prove that for all r>0 and any nonempty open subset ω of Ω the system is approximately controllable on [0, r]. Moreover, we exhibit a sequence of controls steering the system from an initial state to a final state in a prefixed time. As a consequence of this result we obtain the interior approximate controllability of the heat equation by putting a = 0 and b = 1.

Modeling ductile damage of steel in aggressive environment

Kucharski R.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2006

Vol. 10, No 4

417-425

This paper is a proposition of a new damage model, extended to include the influence of the external environment, based on the Gurson yield function and a new damage evolution equation. The model also contains a mass transport equation based on Pick's law. A comparison of experimental and numerical results is included.