Search results for "Boundary"
showing 10 items of 1626 documents
An evolutionary Haar-Rado type theorem
2021
AbstractIn this paper, we study variational solutions to parabolic equations of the type $$\partial _t u - \mathrm {div}_x (D_\xi f(Du)) + D_ug(x,u) = 0$$ ∂ t u - div x ( D ξ f ( D u ) ) + D u g ( x , u ) = 0 , where u attains time-independent boundary values $$u_0$$ u 0 on the parabolic boundary and f, g fulfill convexity assumptions. We establish a Haar-Rado type theorem: If the boundary values $$u_0$$ u 0 admit a modulus of continuity $$\omega $$ ω and the estimate $$|u(x,t)-u_0(\gamma )| \le \omega (|x-\gamma |)$$ | u ( x , t ) - u 0 ( γ ) | ≤ ω ( | x - γ | ) holds, then u admits the same modulus of continuity in the spatial variable.
A sharp stability estimate for tensor tomography in non-positive curvature
2021
Funder: University of Cambridge
On some partial data Calderón type problems with mixed boundary conditions
2021
In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible boundaries. This connects local and nonlocal Calderón type problems. We prove two main results on these type of problems: On the one hand, we derive simultaneous bulk and boundary Runge approximation results. Building on these, we deduce uniqueness for localized bulk and boundary potentials. On the other hand, we construct a family of CGO solutions associated with the corresponding equations. These allow us to deduce uniqueness results for arbitrary bounded, not necessarily localized bulk and boundary potentials. T…
Guaranteed error bounds and local indicators for adaptive solvers using stabilised space-time IgA approximations to parabolic problems
2019
The paper is concerned with space–time IgA approximations to parabolic initial–boundary value problems. We deduce guaranteed and fully computable error bounds adapted to special features of such type of approximations and investigate their efficiency. The derivation of error estimates is based on the analysis of the corresponding integral identity and exploits purely functional arguments in the maximal parabolic regularity setting. The estimates are valid for any approximation from the admissible (energy) class and do not contain mesh-dependent constants. They provide computable and fully guaranteed error bounds for the norms arising in stabilised space–time approximations. Furthermore, a p…
A posteriori error estimates for variational problems in the theory of viscous fluids
2016
The papers included in the thesis are focused on functional type a posteriori error estimates for the Stokes problem, the Stokes problem with friction type boundary conditions, the Oseen problem, and the anti-plane Bingham problem. In the summary of the thesis we consider only the Oseen problem. The papers present and justify special forms of these estimates which are suitable for the approximations generated by the Uzawa algorithm. The estimates are of two main types. Estimates of the first type use exact solutions obtained on the steps of the Uzawa algorithm. They show how errors encompassed in Uzawa approximations behave and have mainly theoretical meaning. Estimates of the second type o…
Aircraft measurements of aerosol particles and trace gases over the Southern Baltic Sea during the BALTIC'15 campaign in 2015
2019
During the BALTIC'15 campaign, conducted in August 2015 over the Southern Baltic Sea, trace gasses (CO2/O3/NOy/SO2) and aerosol particles (number concentration of total/non-volatile/Aitken mode/ Accumulation mode/Coarse mode/refractory black carbon, aerosol extinction coefficient, mass concentration of refractory black carbon were measured). Observations were performed on board of the Alfred Wegener Institute research aircraft Polar 5 during 4 flights: - Scientific flight 1 (SF1) 26 August 2015 - Scientific flight 2 (SF2) 28 August 2015 - Scientific flight 3 (SF3) 28 August 2015 - Scientific flight 4 (SF4) 30 August 2015
Constructing a pedagogical practice across disciplines in pre-service teacher education
2019
In this paper we report a qualitative case study of a teaching intervention in which a pre-service subject teacher pair planned and conducted a course integrating Finnish language and ethics in a multilingual setting. Audio-recorded planning sessions and interviews including learning diaries were analysed using qualitative content analysis to identify the dynamics of collaborative cross-curricular pedagogical practice development and pedagogical language knowledge. The analysis revealed tensions in crossing the boundary between language and content knowledge. The study suggests that when creating cross-curricular practices, student teachers benefit from longer-term processes and theory-base…
Mathematical modelling of problems of mathematical physics with periodic boundary conditions
2014
Darbā izstrādāti jauni speciāli algoritmi parasto un parciālo diferenciālvienādojumu problēmu ar periodiskajiem nosacījumiem skaitliskai modelēšanai, kuri balstās uz precīzā spektra izmantošanu telpisko parciālo atvasinājuma aproksimēšanai ar galīgajām diferencēm. Algoritmi tiek veidoti dažādām divdimensiju matemātiskās fizikas problēmām (lineārām un nelineārām), balstoties uz taišņu metodes algoritmiem un precīzā spektra diferenču shēmām. Izveidotie algoritmi tiek realizēti un salīdzināti ar datorprogrammas MATLAB palīdzību. Ar iegūtajiem algoritmiem tiek risinātas vairākas lietišķas problēmas, t.sk 2D magneto-hidrodinamiska plūsma ap periodiski novietotiem cilindriem, 2D plūsma cilindrā ā…
The Grain Boundary Wetting Phenomena in the Ti‐Containing High‐Entropy Alloys: A Review
2021
This review is written during the preparation of M‐era.Net full proposal ʺGrain boundaries in multicomponent alloys without principal componentʺ (A.K., A.K., G.A.L. and E.R., application No. 9345). The Institute of Solid State Physics, University of Latvia, as a cen‐ ter of excellence, has received funding from the European Union’s Horizon 2020 Framework Pro‐ gramme H2020‐WIDESPREAD‐01‐2016‐2017‐TeamingPhase2 under grant agreement no. 739508, project CAMART2.
BEM analysis of a piezoelectric structural health monitoring system for delamination detection
2013
In the present work a piezoelectric based structural health monitoring (SHM) system is analyzed with the aim of assessing the ability of the piezoelectric patch to detect both edge and embedded delaminations proper of flange-skin composite laminated structures. he boundary element model is developed for piezoelectric solids and is implemented by taking advantage of the multidomain technique to model laminated and cracked configurations. A non-linear spring model interface is then implemented in conjunction with an iterative procedure allowing for the simulation of the finite stiffness of the bonding layers as well as of the non-penetration condition of the delamination surfaces. he dynamic …