The discontinuous Galerkin method for fractional degenerate convection-diffusion equations

We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (L\'evy) operator. We prove various stability estimates along with convergence results toward properly defined (entropy) solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through numerical experiments

Factors perceived to influence exercise adherence in women with breast cancer participating in an exercise programme during adjuvant chemotherapy: a focus group study

Aims and objectives. To explore factors influencing exercise adherence among women with breast cancer while following an exercise programme. Background. Earlier research shows that women with breast cancer decrease physical activity following the cancer diagnosis and that adhering to exercise interventions can be a challenge. Research is needed to identify motivational factors and barriers for exercise adherence among women during treatment for breast cancer. Design. This was a qualitative study to explore patient’s perceptions of the challenges to exercise adherence during a randomised, controlled trial. Methods. Twenty-seven women with early-stage breast cancer were purposively sampled for focus group interviews during 2011–2012 from their participation in the exercise intervention group during 2010–2012. Five focus groups were performed, and data analysis was completed using the systematic text condensation method. Results. During the focus group study, five main themes were identified, which described factors participants perceived to influence their adherence to exercise during chemotherapy: ‘side effects of breast cancer treatment as a barrier to exercise’, ‘restoring and maintaining normality in daily life motivates exercise’, ‘other valued activities compete with exercise’, ‘constructive support enhances exercise’ and ‘positive beliefs about efficacy and outcomes motivate exercise’. Conclusion. Adherence to exercise in women with breast cancer is challenged by internal and external conditions and may be improved by attention to the impact of treatment side effects and by supporting patient self-efficacy towards changing health behaviour. Relevance to clinical practice. Nurses should be aware that exercise adherence could be a challenge among women with breast cancer. They should help identify obstacles to exercise for women and ways to overcome them, as well as support them in their beliefs that they are capable of changing their health behaviou

Exercise: a path to wellness during adjuvant chemotherapy for breast cancer?

Background: Breast cancer treatment can represent a threat to a patient’s wellness. The role of exercise in perceived wellness in women with breast cancer merits further study. Objective: The objective of this study was to describe how exercise is perceived by women to influence their physical and psychosocial wellness at the time they were receiving chemotherapy. Methods: Five focus group interviews with a total of 27 women with early-stage breast cancer were conducted. Prior to the focus groups, the women had participated in an exercise intervention during chemotherapy treatment. Results: Three themes emerged from the analysis: exercise shapes feelings of psychological wellness; exercise stimulates feelings of physical wellness; and exercise influences social wellness. The women reported feeling stronger in a psychological sense after exercising, that the strength exercise improved their upper-limb functioning, and that engaging in exercise triggered social support and interactions. Conclusions: Exercise during breast cancer treatment is perceived to enhance the patients’ wellness on several dimensions and in particular psychological wellness. Exercise might support the patients’ efforts to restore their sense of wellness and enhance their level of daily life functioning. Implications for Practice: Cancer nurses should promote exercise as a wellness-fostering intervention during chemotherapy treatment. Focusing on how exercise can contribute to feelings of wellness may help women with breast cancer choose exercise as a health-promoting activity that contributes to their recovery

A theory of L1L^1-dissipative solvers for scalar conservation laws with discontinuous flux

We propose a general framework for the study of $L^1$ contractive semigroups of solutions to conservation laws with discontinuous flux. Developing the ideas of a number of preceding works we claim that the whole admissibility issue is reduced to the selection of a family of "elementary solutions", which are certain piecewise constant stationary weak solutions. We refer to such a family as a "germ". It is well known that (CL) admits many different $L^1$ contractive semigroups, some of which reflects different physical applications. We revisit a number of the existing admissibility (or entropy) conditions and identify the germs that underly these conditions. We devote specific attention to the anishing viscosity" germ, which is a way to express the "$\Gamma$-condition" of Diehl. For any given germ, we formulate "germ-based" admissibility conditions in the form of a trace condition on the flux discontinuity line $x=0$ (in the spirit of Vol'pert) and in the form of a family of global entropy inequalities (following Kruzhkov and Carrillo). We characterize those germs that lead to the $L^1$-contraction property for the associated admissible solutions. Our approach offers a streamlined and unifying perspective on many of the known entropy conditions, making it possible to recover earlier uniqueness results under weaker conditions than before, and to provide new results for other less studied problems. Several strategies for proving the existence of admissible solutions are discussed, and existence results are given for fluxes satisfying some additional conditions. These are based on convergence results either for the vanishing viscosity method (with standard viscosity or with specific viscosities "adapted" to the choice of a germ), or for specific germ-adapted finite volume schemes

On Nonlinear Stochastic Balance Laws

We are concerned with multidimensional stochastic balance laws. We identify a class of nonlinear balance laws for which uniform spatial $BV$ bounds for vanishing viscosity approximations can be achieved. Moreover, we establish temporal equicontinuity in $L^1$ of the approximations, uniformly in the viscosity coefficient. Using these estimates, we supply a multidimensional existence theory of stochastic entropy solutions. In addition, we establish an error estimate for the stochastic viscosity method, as well as an explicit estimate for the continuous dependence of stochastic entropy solutions on the flux and random source functions. Various further generalizations of the results are discussed

Using Ordinary Digital Cameras in Place of Near-Infrared Sensors to Derive Vegetation Indices for Phenology Studies of High Arctic Vegetation

We thank Mark Gillespie, Nanna Baggesen, and Anne Marit Vik for field assistance. The University in Svalbard (UNIS) provided logistical support. This work was funded by the Norwegian Research Council through the ‘SnoEco’ project (project No. 230970) and Arctic Field Grant (No. 246110/E10). It was supported by the ESA Prodex project ‘Sentinel-2 for High North Vegetation Phenology’ (contract No. 4000110654), the EC FP7 collaborative project ‘Sentinels Synergy Framework’ (SenSyF), funding from The Fram Centre Terrestrial Flagship, also from the EEA Norway Grants (WICLAP project, ID 198571), and from the GRENE Arctic Climate Change Research Project, Ministry of Education, Culture, Sports, Science and Technology in Japan.Peer reviewedPublisher PD

On the upstream mobility scheme for two-phase flow in porous media

When neglecting capillarity, two-phase incompressible flow in porous media is modelled as a scalar nonlinear hyperbolic conservation law. A change in the rock type results in a change of the flux function. Discretizing in one-dimensional with a finite volume method, we investigate two numerical fluxes, an extension of the Godunov flux and the upstream mobility flux, the latter being widely used in hydrogeology and petroleum engineering. Then, in the case of a changing rock type, one can give examples when the upstream mobility flux does not give the right answer.Comment: A preprint to be published in Computational Geoscience