Dataset Information

A Stefan problem on an evolving surface.

ABSTRACT: We formulate a Stefan problem on an evolving hypersurface and study the well posedness of weak solutions given L(1) data. To do this, we first develop function spaces and results to handle equations on evolving surfaces in order to give a natural treatment of the problem. Then, we consider the existence of solutions for L(?) data; this is done by regularization of the nonlinearity. The regularized problem is solved by a fixed point theorem and then uniform estimates are obtained in order to pass to the limit. By using a duality method, we show continuous dependence, which allows us to extend the results to L(1) data.

SUBMITTER: Alphonse A

PROVIDER: S-EPMC4535267 | biostudies-literature | 2015 Sep

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

A Stefan problem on an evolving surface.

Alphonse Amal A Elliott Charles M CM

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences 20150901 2050

We formulate a Stefan problem on an evolving hypersurface and study the well posedness of weak solutions given L(1) data. To do this, we first develop function spaces and results to handle equations on evolving surfaces in order to give a natural treatment of the problem. Then, we consider the existence of solutions for L(∞) data; this is done by regularization of the nonlinearity. The regularized problem is solved by a fixed point theorem and then uniform estimates are obtained in order to pass ...[more]

PMID: 26261364

Similar Datasets

Project description:UnlabelledBackgroundHepatitis B virus (HBV) is a common cause of viral hepatitis with significant health complications including cirrhosis and hepatocellular carcinoma. Assays for hepatitis B surface antigen (HBsAg) are the most frequently used tests to detect HBV infection. Vaccination for HBV can produce transiently detectable levels of HBsAg in patients. However, the time course and duration of this effect is unclear. The objective of this retrospective study was to clarify the frequency and duration of transient HBsAg positivity following vaccination against HBV.MethodsThe electronic medical record at an academic tertiary care medical center was searched to identify all orders for HBsAg within a 17 month time period. Detailed chart review was performed to identify all patients who were administered HBV vaccine within 180 days prior to HBsAg testing and also to ascertain likely cause of weakly positive (grayzone) results.ResultsDuring the 17 month study period, 11,719 HBsAg tests were ordered on 9,930 patients. There were 34 tests performed on 34 patients who received HBV vaccine 14 days or less prior to HBsAg testing. Of these 34 patients, 11 had grayzone results for HBsAg that could be attributed to recent vaccination. Ten of the 11 patients were renal dialysis patients who were receiving HBsAg testing as part of routine and ongoing monitoring. Beyond 14 days, there were no reactive or grayzone HBsAg tests that could be attributed to recent HBV vaccination. HBsAg results reached a peak COI two to three days following vaccination before decaying. Further analysis of all the grayzone results within the 17 month study period (43 results out of 11,719 tests) revealed that only 4 of 43 were the result of true HBV infection as verified by confirmatory testing.ConclusionsOur study confirms that transient HBsAg positivity can occur in patients following HBV vaccination. The results suggest this positivity is unlikely to persist beyond 14 days post-vaccination. Our study also demonstrates that weakly positive HBsAg results often do not reflect actual HBV infection, underscoring the importance of confirmatory testing. This study also emphasizes that vaccination-induced HBsAg positives occur most commonly in hemodialysis patients.

Dataset Information

A Stefan problem on an evolving surface.

Publications

A Stefan problem on an evolving surface.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets