Strong traces to degenerate parabolic equations

We prove existence of strong traces at $t=0$ for quasi-solutions to the degenerate parabolic equations under non-degeneracy assumptions. In order to solve the problem, we introduce a defect measure type functional and combine it with the blow up method

On a new class of functional spaces with application to the velocity averaging

We introduce a new family of functional spaces which incorporate Bochner spaces Lp(Rm; E), with E being an appropriate Banach space, and to which we extend the H-distributions. We use the developed theory to prove a general version of the velocity averaging lemma in a heterogeneous Lp, p ≤ 2 setting

Degenerate parabolic equations -- compactness and regularity of solutions

We introduce a new method which resolves the problem of regularity and compactness of entropy solutions for nonlinear degenerate parabolic equations under non-degeneracy conditions on the sphere. In particular, we address a problem of regularity of entropy solutions to homogeneous (autonomous) degenerate parabolic PDEs and existence of weak solutions to heterogeneous degenerate parabolic PDEs (non-autonomous PDEs -- with flux and diffusion explicitly depending on the space and time variables). The method of proof is reduction of the equation to a specific kinetic formulation involving two transport equations, one of the second and one of the first order. In the heterogeneous situation, this enables us to use (variants of) the H-measures to get velocity averaging lemmas and then, consequently, existence of a weak solution. In the homogeneous case, the kinetic reformulation makes it possible to get necessary estimates of the solution on the Littlewood-Paley dyadic blocks of the dual space.Comment: 32 page

Control theory for nonlinear fractional dispersive systems

We consider a terminal control problem for processes governed by a nonlinear system of fractional ODEs. In order to show existence of the control, we first consider the linear counterpart of the system and reprove a number of classical theorems in the fractional setting (representation of the solution through the Gramian type matrix, Kalman's principle, equivalence of the controllability and observability). We are then in the position to use a fixed point theorem approach and various techniques from the fractional calculus theory to get the desired result

Velocity averaging for diffusive transport equations with discontinuous flux

We consider a diffusive transport equation with discontinuous flux and prove the velocity averaging result under non-degeneracy conditions. As a corollary, we show the existence of a solution for the Cauchy problem for nonlinear degenerate parabolic equation with discontinuous flux. In order to achieve the results, we introduce a new variant of micro-local defect functionals which are able to "recognise" changes of the type of the equation

Velocity averaging under minimal conditions for deterministic and stochastic kinetic equations with irregular drift

This study investigates the $L^1_{\operatorname{loc}}$ compactness of velocity averages of sequences of solutions $\{u_n\}$ for a class of kinetic equations. The equations are examined within both deterministic and stochastic heterogeneous environments. The primary objective is to deduce velocity averaging results under conditions on $u_n$ and the drift ${\mathfrak f}={\mathfrak f}(t,{\boldsymbol x},{\boldsymbol \lambda})$ that are more lenient than those stipulated in previous studies. The main outcome permits the inclusion of highly irregular drift vectors ${\mathfrak f} \in L^q$ that adhere to a general non-degeneracy condition. Moreover, the sequence $\{u_n\}$ is uniformly bounded in $L^p$ -- for an exponent $p$ allowed to be strictly smaller than $2$ -- under the requirement $\frac{1}{p} + \frac{1}{q} < 1$. Resolving the matter of strong compactness in velocity averages, considering these assumptions, has remained an open problem for a long time. The cornerstone of our work's progress lies in the strategic employment of the broader concept of $H$-distributions, moving beyond the traditional reliance on $H$-measures. Notably, our study represents one of the first significant uses of $H$-distributions in this context

OBRANA GRAĐEVINSKIH KONSTRUKCIJA OD POTRESA POSTUPKOM IZOLACIJE - BUDUĆNOST ILI UTOPIJA

Ovaj rad sažeti je prikaz postupka seizmičke izolacije građevinskih konstrukcija, argumentiran kratkim prikazom provedenih seizmičkih analiza. Dio je diplomskog rada studentice Senke Mitrović, obranjenog u listopadu 2005. godine na Građevinskom fakultetu Osijek. Hoće li jednog dana ovaj način zaštite građevinskih konstrukcija postati uobičajen u inženjerskoj praksi u Hrvatskoj (kao u nekim slučajevima danas u Japanu) ili je u pitanju samo postupak zasnovan na teoriji dinamike konstrukcija, pokazat će vrijeme. Osim osnova na kojima se zaštita zasniva prikazan je i kratki dio numeričkog postupka provedenog za armiranobetonsku okvirnu konstrukciju tlocrtne površine 30x18 metara i visine 18 metara

PHYSICAL ASSET MANAGEMENT IN EVERYDAY LIFE

Svrha rada je pokušati dobiti odgovor na pitanje može li Gospodarenje imovinom imati primjenu u svakodnevnom životu. Kako bi to ispitali provedeno je istraživanje. U istraživanju su ispitanicima korištenjem studija slučaja simulirane situacije u kojima moraju donositi odluke. Istraživanje je provedeno u tri grupe od 114 ispitanika. Svaka od tri grupe dobila je različite studije slučaja, a svima je zajedničko da donose odluku o rješavanjima identičnih problema na imovini koja je također jednaka u sve tri grupe. Analiza rezultata pokazala je velika odstupanja između pojedinih grupa. Daljnjom analizom utvrđeno je kako su same pretpostavke iz studija slučaja, koje nisu bile vezane direktno za stanje imovine, imale ključan utjecaj na odstupanja. Kao ključni čimbenik identificirana je kompleksnost situacija u pojedinim grupama. Nije dobiven jednoznačan odgovor na temeljno pitanje, ali je određeno u kojim situacijama ipak ima mjesta za primjenu Gospodarenja imovinom u svakodnevnom životu.The scope of this paper is to find answer on the question “Is Physical Asset Management applicable in everyday life? To find out the answer on this question research is conducted. In this research examinees were asked to make decisions based on data from case studies. The research has been conducted on three groups of 114 examinees. Each group received different case studies, but all the case studies have in common making decision on same problems on the same assets. Analysis showed significant deviations between groups. Deeper analysis showed that facts not directly connected with Physical Assets have key impact on those differences. Complexity of situation is identified as key contributor of deviation between groups. Unambiguous answer to basic question is not found. However, situations where Physical Asset Management is applicable are defined

Elemental composition of moss and lichen species in eastern Serbia

Instrumental neutron activation analysis is used to determine a content of 47 elements (Na, Mg, Al, Cl, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Ni, Co, Cu, Zn, As, Se, Br, Rb, Sr, Zr, Mo, Ag, Cd, Sb, I, Ba, Cs, La, Ce, Nd, Sm, Eu, Gd, Tb, Dy, Tm, Yb, Lu, Hf, Ta, W, Au, Hg, Th, and U) in mosses (Homolothecium sp., Hypnum cupressiforme Hedw., and Brachythecium mildeanum (Schimp.) Schimp.) and lichen (Cladonia fimbriata (L.) Fr.) collected in three locations in Eastern Serbia over years 2006-2010. Concentrations of six elements (Zr, Nd, Gd, Tm, Yb, and Lu) in mosses in Serbia are measured for the first time. For other elements, the obtained concentrations fall within the ranges reported for mosses and lichens in Europe, but no declining trend in concentrations of V, Cd, Cr, Zn, Ni, Fe, and Cu, that has been described in the literature, can be inferred from our results. Factor analysis shows that terrigenous and industrial components are the highest contributing factors to the elemental composition and that the most polluted measurement site is in the vicinity of a copper mining and smelting complex