Giorgi Techniques Research Articles

Global existence and convergence rates to a chemotaxis-fluids system with mixed boundary conditions

In this paper, we investigate the large time behavior of strong solutions to a chemotaxis-fluids system in an unbounded domain with mixed boundary conditions. Based on the anisotropic Lp technique, the elliptic estimates and Stokes estimates, we first establish the global existence of strong solution around the equilibrium state (0,csatn,0) with the help of the continuity arguments, where csatn is the saturation value of oxygen inside the fluid. Then we use De Giorgi's technique and energy method to show that such a solution will converge to (0,csatn,0) with an explicit convergence rate in the chemotaxis-free case. Our assumptions and results are consistent with the experimental descriptions and the numerical analysis. The novelty here consists of deriving some new elliptic estimates and Stokes estimates, and choosing a suitable weight in De Giorgi's technique to deal with the mixed boundary conditions.

Patients' experiences with cholecystitis and a cholecystectomy.

Nurses commonly care for patients with cholecystitis, a major health problem with a growing prevalence. Although considerable research has been done to compare patient outcomes among surgical approaches for cholecystitis, few studies have examined the experiences of patients with cholecystitis and the subsequent cholecystectomy surgery. A qualitative study with a phenomenological approach was initiated to better understand the experience of hospitalized patients with cholecystitis through their cholecystectomy surgery. Face-to-face semistructured interviews were conducted with patients diagnosed with cholecystitis and scheduled for a cholecystectomy at a rural, Midwestern hospital in the United States. Postoperative interviews were then conducted with the patients who experienced an uneventful cholecystectomy. Giorgi's technique was used to analyze postoperative narratives of the patients' cholecystectomy experiences to determine the themes. Following analysis of interview transcripts from the patients, 5 themes emerged: (a) consumed by discomfort and pain, (b) restless discomfort interrupting sleep, (c) living in uncertainty, (d) impatience to return to normalcy, and (e) feelings of vulnerability. Informants with acute cholecystitis described distressing pain before and after surgery that interfered with sleep and family responsibilities. Increased awareness is needed to prevent the disruption to daily life that can result from the cholecystitis and resulting cholecystectomy surgery. Also, nurses can help ease the unpredictability of the experience by providing relevant patient education, prompt pain relief, and an attentive approach to the nursing care.

Regularization in Keller-Segel type systems and the De Giorgi method

Fokker-Planck systems modeling chemotaxis, haptotaxis and angiogenesis are numerous and have been widely studied. Several results exist that concern the gain of L p integrability but methods for proving regularizing effects in L ∞ are still very few. Here, we consider a special example, related to the Keller-Segel system, which is both illuminating and singular by lack of diffusion on the second equation (the chemical concentration). We show the gain of L ∞ integrability (strong hypercontractivity) when the initial data belongs to the scale-invariant space. Our proof is based on De Giorgi's technique for parabolic equations. We present this technique in a formalism which might be easier that the usual iteration method. It uses an additional continuous parameter and makes the relation to kinetic formulations for hyperbolic conservation laws.

Global and nonglobal weak solutions to a degenerate parabolic system

This paper deals with a degenerate parabolic system coupled via general reaction terms of power type. Global weak solutions are obtained by means of energy estimates and the De Giorgi's technique. In particular, the criterion for global nonexistence of weak solutions is proved by introducing suitable weak sub-solutions together with a weak comparison principle. In summary, the critical exponent for weak solutions of the degenerate parabolic system is determined.

Nursing students' perspectives: experiences of caring and not-so-caring interactions with faculty.

The purpose of this study was to describe the meaning of baccalaureate nursing students' lived experience of caring and not-so-caring interactions with faculty. The research questions explored the phenomenon of being cared-for or not-cared-for by asking, "What does being cared-for by faculty mean to baccalaureate nursing students?" Students were also asked to describe not-so caring interactions with faculty. Seventeen baccalaureate nursing students at a private liberal arts college and 15 baccalaureate nursing students at a public university were interviewed. Transcripts of the tape-recorded interviews were analyzed using Giorgi's technique. After reflection upon the content of the interviews, significant statements were identified, meaning units were developed, and themes were extracted which were then abstracted into categories of Recognition, Connection, and Confirmation/Affirmation. Finally, general structural descriptions of phenomena of a caring and of a not-so-caring interaction were constructed. Implications for teaching, research, and practice are described.