Asymptotic expansions of the solutions of the Cauchy problem for nonlinear parabolic equations

Let $u$ be a solution of the Cauchy problem for the nonlinear parabolic equation $$\partial_t u=\Delta u+F(x,t,u,\nabla u) \quad in \quad{\bf R}^N\times(0,\infty), \quad u(x,0)=\varphi(x)\quad in \quad{\bf R}^N,$$ and assume that the solution $u$ behaves like the Gauss kernel as $t\to\infty$. In this paper, under suitable assumptions of the reaction term $F$ and the initial function $\varphi$, we establish the method of obtaining higher order asymptotic expansions of the solution $u$ as $t\to\infty$. This paper is a generalization of our previous paper, and our arguments are applicable to the large class of nonlinear parabolic equations

Asymptotic behaviour of a semilinear elliptic system with a large exponent

Consider the problem \begin{eqnarray*} -\Delta u &=& v^{\frac 2{N-2}},\quad v>0\quad {in}\quad \Omega, -\Delta v &=& u^{p},\:\:\:\quad u>0\quad {in}\quad \Omega, u&=&v\:\:=\:\:0 \quad {on}\quad \partial \Omega, \end{eqnarray*} where $\Omega$ is a bounded convex domain in $\R^N,$ $N>2,$ with smooth boundary $\partial \Omega.$ We study the asymptotic behaviour of the least energy solutions of this system as $p\to \infty.$ We show that the solution remain bounded for $p$ large and have one or two peaks away form the boundary. When one peak occurs we characterize its location.Comment: 16 pages, submmited for publicatio

How about your peers? Cystic fibrosis questionnaire data from healthy children and adolescents

Contains fulltext : 97967.pdf (publisher's version ) (Open Access)BACKGROUND: The Cystic Fibrosis Questionnaire (CFQ) is widely used in research as an instrument to measure quality of life in patients with cystic fibrosis (CF). In routine patient care however, measuring quality of life is still not implemented in guidelines. One of the reasons might be the lack of consensus on how to interpret CFQ scores of an individual patient, because appropriate reference data are lacking. The question which scores reflect normal functioning and which scores reflect clinically relevant problems is still unanswered. Moreover, there is no knowledge about how healthy children and adolescents report on their quality of life (on the CFQ). With regard to quality of life the effect of normal development should be taken into account, especially in childhood and adolescence. Therefore, it is important to gain more knowledge about how healthy children and adolescents report on their quality of life and if there are any difference in a healthy populations based on age or gender. Without these data we cannot adequately interpret the CFQ as a tool in clinical care to provide patient-tailored care. Therefore this study collected data of the CFQ in healthy children and adolescents with the aim to refer health status of CF youngsters to that of healthy peers. METHODS: The CFQ was completed by 478 healthy Dutch children and adolescents (aged 6-20) in a cross-sectional study. RESULTS: The majority of healthy children (over 65%) did not reach maximum scores on most domains of the CFQ. Median CFQ-scores of healthy children and adolescents ranged from 67 to 100 (on a scale of 0-100) on the different CFQ-domains. Significant differences in quality of life exist among healthy children and adolescents, and these depend on age and gender. CONCLUSIONS: Reference data of quality of life scores from a healthy population are essential for adequate interpretation of quality of life in young patients with CF. Clinicians should be aware that the perception of health-related quality of life is not as disease-specific as one might think and also relies on factors such as age, normal maturation and gender

Case Report: Dual nebulised antibiotics among adults with cystic fibrosis and chronic Pseudomonas infection [version 2; referees: 1 approved, 2 approved with reservations]

Pulmonary exacerbations in adults with cystic fibrosis (CF) and chronic Pseudomonas aeruginosa (Psae) infection are usually treated with dual intravenous antibiotics for 14 days, despite the lack of evidence for best practice. Intravenous antibiotics are commonly associated with various systemic adverse effects, including renal failure and ototoxicity. Inhaled antibiotics are less likely to cause systematic adverse effects, yet can achieve airway concentrations well above conventional minimum inhibitory concentrations. Typically one inhaled antibiotic is used at a time, but dual inhaled antibiotics (i.e. concomitant use of two different inhaled antibiotics) may have synergistic effect and achieve better results in the treatment of exacerbations. We presented anecdotal evidence for the use of dual inhaled antibiotics as an acute treatment for exacerbations, in the form of a case report. A female in her early thirties with CF and chronic Psae infection improved her FEV1 by 5% and 2% with two courses of dual inhaled antibiotics to treat exacerbations in 2016. In contrast, her FEV1 changed by 2%, –2%, 0% and 2%, respectively, with four courses of dual intravenous antibiotics in 2016. Baseline FEV1 was similar prior to all six courses of treatments. The greater FEV1 improvements with dual inhaled antibiotics compared to dual intravenous antibiotics suggest the potential role of using dual inhaled antibiotics to treat exacerbations among adults with CF and chronic Psae infection, especially since a greater choice of inhaled anti-pseudomonal antibiotics is now available. A previous study in 1985 has looked at the concomitant administration of inhaled tobramycin and carbenicillin, by reconstituting antibiotics designed for parenteral administration. To our knowledge, this is the first literature to describe the concomitant use of two different antibiotics specifically developed for delivery via the inhaled route

Adherence with tobramycin inhaled solution and health care utilization

<p>Abstract</p> <p>Background</p> <p>Adherence with tobramycin inhalation solution (TIS) during routine cystic fibrosis (CF) care may differ from recommended guidelines and affect health care utilization.</p> <p>Methods</p> <p>We analyzed 2001-2006 healthcare claims data from 45 large employers. Study subjects had diagnoses of CF and at least 1 prescription for TIS. We measured adherence as the number of TIS therapy cycles completed during the year and categorized overall adherence as: low ≤ 2 cycles, medium >2 to <4 cycles, and high ≥ 4 cycles per year. Interquartile ranges (IQR) were created for health care utilization and logistic regression analysis of hospitalization risk was conducted by TIS adherence categories.</p> <p>Results</p> <p>Among 804 individuals identified with CF and a prescription for TIS, only 7% (n = 54) received ≥ 4 cycles of TIS per year. High adherence with TIS was associated with a decreased risk of hospitalization when compared to individuals receiving ≤ 2 cycles (adjusted odds ratio 0.40; 95% confidence interval 0.19-0.84). High adherence with TIS was also associated with lower outpatient service costs (IQR: $2,159-$8444 vs. $2,410-$14,423) and higher outpatient prescription drug costs (IQR: $35,125-$60,969 vs. $10,353-$46,768).</p> <p>Conclusions</p> <p>Use of TIS did not reflect recommended guidelines and may impact other health care utilization.</p

Efficacy and safety of azithromycin maintenance therapy in primary ciliary dyskinesia (BESTCILIA): a multicentre, double-blind, randomised, placebo-controlled phase 3 trial.

BACKGROUND Use of maintenance antibiotic therapy with the macrolide azithromycin is increasing in a number of chronic respiratory disorders including primary ciliary dyskinesia (PCD). However, evidence for its efficacy in PCD is lacking. We aimed to determine the efficacy and safety of azithromycin maintenance therapy for 6 months in patients with PCD. METHODS The Better Experimental Screening and Treatment for Primary Ciliary Dyskinesia (BESTCILIA) trial was a multicentre, double-blind, parallel group, randomised, placebo-controlled phase 3 trial done at 6 European PCD clinics (tertiary paediatric care centres and university hospitals in Denmark, Germany, Netherlands, Switzerland, and UK). Patients with a confirmed diagnosis of PCD, aged 7-50 years old, and predicted FEV1 greater than 40% were recruited. Participants were randomly assigned (1:1), stratified by age and study site, via a web-based randomisation system to azithromycin 250 mg or 500 mg as tablets according to bodyweight (</≥ 40 kg) or identical placebo, three times a week for 6 months. The random allocation sequence was a permuted block randomisation, with a block size of four, generated by an external consultancy. Participants, investigators, and care providers were masked to treatment allocation. The primary endpoint was the number of respiratory exacerbations over 6 months. Analysis was by intention to treat. This study is registered in the EU Clinical Trials Register, EudraCT number 2013-004664-58. FINDINGS Between June 24, 2014, and Aug 23, 2016, 102 patients were screened, of whom 90 were randomly assigned to either azithromycin (n=49) or placebo (n=41). The study was ended without having included the planned number of participants due to recruitment difficulties. The mean number of respiratory exacerbations over 6 months was 0·75 (SD 1·12) in the azithromycin group compared with 1·62 (1·64) in the placebo group, and participants receiving azithromycin had significantly lower rate of exacerbations during the individual treatment periods (rate ratio 0·45 [95% CI 0·26-0·78]; p=0·004). Four serious adverse events were reported, occurring in one (2%) of 47 participants in the azithromycin group and in three (7%) of 41 participants in the placebo group. Loose stools or diarrhoea were more common in the azithromycin group than in the placebo group (11 [23%] vs two [5%]). INTERPRETATION This first multinational randomised controlled trial on pharmacotherapy in PCD showed that azithromycin maintenance therapy for 6 months was well tolerated and halved the rate of respiratory exacerbations. Azithromycin maintenance therapy is an option for patients with PCD with frequent exacerbations potentially leading to reduced need for additional antibiotic treatments and preventing irreversible lung damage. FUNDING European Commission Seventh Framework Programme and Children's Lung Foundation (Denmark)

Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach

Five types of blow-up patterns that can occur for the 4th-order semilinear parabolic equation of reaction-diffusion type u_t= -\Delta^2 u + |u|^{p-1} u \quad {in} \quad \ren \times (0,T), p>1, \quad \lim_{t \to T^-}\sup_{x \in \ren} |u(x,t)|= +\iy, are discussed. For the semilinear heat equation $u_t= \Delta u+ u^p$, various blow-up patterns were under scrutiny since 1980s, while the case of higher-order diffusion was studied much less, regardless a wide range of its application.Comment: 41 pages, 27 figure

Antibiotic strategies for eradicating Pseudomonas aeruginosa in people with cystic fibrosis

Background: Respiratory tract infection with Pseudomonas aeruginosa occurs inmost people with cystic fibrosis. Once chronic infection is established, Pseudomonas aeruginosa is virtually impossible to eradicate and is associated with increased mortality and morbidity. Early infection may be easier to eradicate. This is an update of a Cochrane review first published in 2003, and previously updated in 2006 and 2009. Objectives: To determine whether antibiotic treatment of early Pseudomonas aeruginosa infection in children and adults with cystic fibrosis eradicates the organism, delays the onset of chronic infection, and results in clinical improvement. To evaluate whether there is evidence that a particular antibiotic strategy is superior to or more cost-effective than other strategies and to compare the adverse effects of different antibiotic strategies (including respiratory infection with other micro-organisms). Search methods: We searched the Cochrane Cystic Fibrosis and Genetic Disorders Group Trials Register comprising references identified from comprehensive electronic database searches and handsearches of relevant journals and abstract books of conference proceedings. Most recent search: 08 September 2014. Selection criteria: We included randomised controlled trials of people with cystic fibrosis, in whom Pseudomonas aeruginosa had recently been isolated from respiratory secretions. We compared combinations of inhaled, oral or intravenous antibiotics with placebo, usual treatment or other combinations of inhaled, oral or intravenous antibiotics. We excluded non-randomised trials, cross-over trials, and those utilising historical controls. Data collection and analysis: Both authors independently selected trials, assessed risk of bias and extracted data. Main results: The search identified 49 trials; seven trials (744 participants) with a duration between 28 days and 27 months were eligible for inclusion. Three of the trials are over 10 years old and their results may be less applicable today given the changes in standard treatment. Some of the trials had low numbers of participants and most had relatively short follow-up periods; however, there was generally a low risk of bias from missing data. In most trials it was difficult to blind participants and clinicians to treatment given the interventions and comparators used. Two trials were supported by the manufacturers of the antibiotic used. Evidence from two trials (38 participants) at the two-month time-point showed treatment of early Pseudomonas aeruginosa infection with inhaled tobramycin results in microbiological eradication of the organism from respiratory secretions more often than placebo, odds ratio 0.15 (95% confidence interval 0.03 to 0.65) and data from one of these trials, with longer follow up, suggested that this effect may persist for up to 12 months. One randomised controlled trial (26 participants) compared oral ciprofloxacin and nebulised colistin versus usual treatment. Results after two years suggested treatment of early infection results in microbiological eradication of Pseudomonas aeruginosa more often than no anti-pseudomonal treatment, odds ratio 0.12 (95% confidence interval 0.02 to 0.79). One trial comparing 28 days to 56 days treatment with nebulised tobramycin solution for inhalation in 88 participants showed that both treatments were effective and well-tolerated, with no notable additional improvement with longer over shorter duration of therapy. However, this trial was not powered to detect non- inferiority or equivalence. A trial of oral ciprofloxacin with inhaled colistin versus nebulised tobramycin solution for inhalation alone (223 participants) failed to show a difference between the two strategies, although it was underpowered to show this. A further trial of inhaled colistin with oral ciprofloxacin versus nebulised tobramycin solution for inhalation with oral ciprofloxacin also showed no superiority of the former, with increased isolation of Stenotrophomonas maltophilia in both groups. A recent, large trial in 306 children aged between one and 12 years compared cycled nebulised tobramycin solution for inhalation to culture-based therapy and also ciprofloxacin to placebo. The primary analysis showed no difference in time to pulmonary exacerbation or proportion of Pseudomonas aeruginosa positive cultures. An analysis performed in this review (not adjusted for age) showed fewer participants in the cycled therapy group with one or more isolates of Pseudomonas aeruginosa, odds ratio 0.51 (95% CI 0.31 to 0.28). Authors’ conclusions: We found that nebulised antibiotics, alone or in combination with oral antibiotics, were better than no treatment for early infection with Pseudomonas aeruginosa. Eradication may be sustained for up to two years. There is insufficient evidence to determine whether antibiotic strategies for the eradication of early Pseudomonas aeruginosa decrease mortality or morbidity, improve quality of life, or are associated with adverse effects compared to placebo or standard treatment. Four trials of two active treatments have failed to show differences in rates of eradication of Pseudomonas aeruginosa. There have been no published randomised controlled trials that investigate the efficacy of intravenous antibiotics to eradicate Pseudomonas aeruginosa in cystic fibrosis. Overall, there is still insufficient evidence from this review to state which antibiotic strategy should be used for the eradication of early Pseudomonas aeruginosa infection in cystic fibrosis