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• 1.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Homogenization of some parabolic operators with several time scales2007In: Applications of Mathematics, ISSN 0862-7940, E-ISSN 1572-9109, Vol. 52, no 5, p. 431-446Article in journal (Refereed)

The main focus in this paper is on homogenization of a parabolic problem with two local time scales. Under certain assumptions on the coefficient a, there exists a G-limit b, which we characterize by means of multiscale techniques for r>0, r≠1. Also, an interpretation of asymptotic expansions in the context of two-scale convergence is made.

• 2.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
Homogenization of a linear parabolic problem with a certain type of matching between the microscopic scales2018In: Applications of Mathematics, ISSN 0862-7940, E-ISSN 1572-9109, Vol. 63, no 5, p. 503-521Article in journal (Refereed)

This paper is devoted to the study of the linear parabolic problem $\varepsilon\partial_tu_{\varepsilon}\left(x,t\right)-\nabla\cdot\left(a\left(x/\varepsilon,t/\varepsilon^3\right)\nabla u_{\varepsilon}\left(x,t\right)\right)=f\left(x,t\right)$ by means of periodic homogenization. Two interesting phenomena arise as a result of the appearance of the coefficient $\varepsilon$ in front of the timederivative. First, we have an elliptic homogenized problem although the problem studiedis parabolic. Secondly, we get a parabolic local problem even though the problem has adifferent relation between the spatial and temporal scales than those normally giving rise to parabolic local problems. To be able to establish the homogenization result, adapting to the problem we state and prove compactness results for the evolution setting of multiscale and very weak multiscale convergence. In particular, assumptions on the sequence $\left{u_{\varepsilon}\right}$ different from the standard setting are used, which means that these results are also of independent interest.

• 3.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.
Homogenization of monotone parabolic problems with several temporal scales2012In: Applications of Mathematics, ISSN 0862-7940, E-ISSN 1572-9109, Vol. 57, no 3, p. 191-214Article in journal (Refereed)

In this paper we homogenize monotone parabolic problems with two spatial scales and any number of temporal scales. Under the assumption that the spatial and temporal scales are well-separated in the sense explained in the paper, we show that there is an H-limit defined by at most four distinct sets of local problems corresponding to slow temporal oscillations, slow resonant spatial and temporal oscillations (the “slow” self-similar case), rapid temporal oscillations, and rapid resonant spatial and temporal oscillations (the “rapid” self-similar case), respectively.

• 4.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
On general two-scale convergence and its application to the characterization of G-limits2007In: Applications of Mathematics, ISSN 0862-7940, E-ISSN 1572-9109, Vol. 52, no 4, p. 285-302Article in journal (Refereed)

We characterize some G-limits using two-scale techniques and investigate a method to detect deviations from the arithmetic mean in the obtained G-limit, where no peirodicity assumptions are involved. We also prove some results on the properties of generalized two-scale convergence.

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