### On non-variational solutions to optimal boundary control problems for parabolic equations

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

Adams R. *Sobolev spaces*, Academic Press, New York, 1975.

Buttazzo G., Kogut P.I. "Weak optimal controls in coefficients for linear elliptic problems", *Revista Matematica Complutense*, 2011; 24: pp. 83-94.

Gorbonos S.O., Kogut P.I. "Variational solutions of an optimal control problem with unbounded coefficient", *Visnyk DNU. Series: Mathematical Modelling*, DNU, Dnipropetrovsk, 2013; 5(8): pp. 69-83. (in Ukrainian)

Ivanenko V.I., Mel’nik V.S. *Variational Methods in Optimal Control Problems for Systems with Distributed Parameters*, Naukova Dumka, Kyiv, 1988. (in Russian)

Fannjiang M.A., Papanicolaou G.C. "Diffusion in turbulence", *Probab. Theory and Related Fields*, 1996; 105: pp. 279-334.

Fursikov A.V. *Optimal Control of Distributed Systems. Theory and Applications*, AMS, Providence, RI, 2000.

Kogut P.I. "On Approximation of an Optimal Boundary Control Problem for Linear Elliptic Equation with Unbounded Coefficients", *Discrete and Continuous Dynamical Systems — Series A*, 2014; 34(5): pp. 2105-2133.

Kogut P.I., Leugering G. *Optimal Control Problems for Partial Differential Equations on Reticulated Domains: Approximation and Asymptotic Analysis*, Birkhauser, Boston, 2011.

Jin T., Mazya V., Schaftinger J. van. "Pathological solutions to elliptic problems in divergence form with continuous coefficients", *C. R. Math. Acad. Sci. Paris*, 2009; 347(13-14): pp. 773-778.

Salsa S. *Partial Differential Equations in Action: From Modelling to Theory*, Springer-Verlag, Milan, 2008.

Serrin J. "Pathological solutions of elliptic differential equations", *Ann. Scuola Norm. Sup. Pisa*, 1964; 3(18): pp. 385-387.

Zhikov V.V. "Diffusion in incompressible random ﬂow", *Functional Analysis and Its Applications*, 1997; 31(3): pp. 156-166.

Zhikov V.V. "Remarks on the uniqueness of a solution of the Dirichlet problem for second-order elliptic equations with lower-order terms", *Functional Analysis and Its Applications*, 2004; 38(3): pp. 173-183.

Vazquez J.L., Zuazua E. "The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential", *J. of Functional Analysis*, 2000; 173: pp. 103-153.

DOI: https://dx.doi.org/10.15421/241405

### Refbacks

- There are currently no refbacks.

Copyright (c) 2014 S.O. Gorbonos, P.I. Kogut

This work is licensed under a Creative Commons Attribution 4.0 International License.