Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case

We consider a possibly degenerate porous media type equation over all of $\R^d$ with $d = 1$, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. This equation is motivated by some singular behaviour arising in complex self-organized critical systems. The main idea consists in approximating the equation by equations with monotone non-degenerate coefficients and deriving some new analytical properties of the solution

Global attractors for Cahn-Hilliard equations with non constant mobility

We address, in a three-dimensional spatial setting, both the viscous and the standard Cahn-Hilliard equation with a nonconstant mobility coefficient. As it was shown in J.W. Barrett and J.W. Blowey, Math. Comp., 68 (1999), 487-517, one cannot expect uniqueness of the solution to the related initial and boundary value problems. Nevertheless, referring to J. Ball's theory of generalized semiflows, we are able to prove existence of compact quasi-invariant global attractors for the associated dynamical processes settled in the natural "finite energy" space. A key point in the proof is a careful use of the energy equality, combined with the derivation of a "local compactness" estimate for systems with supercritical nonlinearities, which may have an independent interest. Under growth restrictions on the configuration potential, we also show existence of a compact global attractor for the semiflow generated by the (weaker) solutions to the nonviscous equation characterized by a "finite entropy" condition

Random attractors for degenerate stochastic partial differential equations

We prove the existence of random attractors for a large class of degenerate stochastic partial differential equations (SPDE) perturbed by joint additive Wiener noise and real, linear multiplicative Brownian noise, assuming only the standard assumptions of the variational approach to SPDE with compact embeddings in the associated Gelfand triple. This allows spatially much rougher noise than in known results. The approach is based on a construction of strictly stationary solutions to related strongly monotone SPDE. Applications include stochastic generalized porous media equations, stochastic generalized degenerate p-Laplace equations and stochastic reaction diffusion equations. For perturbed, degenerate p-Laplace equations we prove that the deterministic, infinite dimensional attractor collapses to a single random point if enough noise is added.Comment: 34 pages; The final publication is available at http://link.springer.com/article/10.1007%2Fs10884-013-9294-

The role of pancreatic islands transplantation in the management of chronic conditions

Institutul Clinic Fundeni, România, București, Al XIII-lea Congres al Asociației Chirurgilor „Nicolae Anestiadi” și al III-lea Congres al Societății de Endoscopie, Chirurgie miniminvazivă și Ultrasonografie ”V.M.Guțu” din Republica MoldovaIntroducere: Diabetul zaharat reprezintă o problemă de sănătate la nivel mondial, în primul rând datorită numarului mare de pacienți (se estimează că în 2015, 1 din 11 adulți suferea de diabet așteptându-se ca până în 2040, 1 din 10 adulți să fie diabetic); în al doilea rând, mortalitatea prin diabet depașește mortalitatea sumată prin boli răspândite ca malaria, HIV/SIDA și tuberculoza; nu în ultimul rand, costurile sistemelor de sănătate pentru o persoană diabetică sunt de 2.3 ori mai mari decât pentru o persoană nondiabetică. Transplantul de insule pancreatice ca terapie în diabetul zaharat, reprezintă o metodă sigură și eficientă, care implică o intervenție chirurgicală relativ ușoara, cu o morbiditate scăzuta și o mortalitate aproape de 0, în comparație cu transplantul de pancreas integral. Rezultatele depind însa de procesul de izolare a insulelor pancreatice, un proces complex, care implică costuri ridicate. Material și metode: Între anii 2007-2012 au avut loc 20 de recoltari în bloc spleno-pancreatico-duodenale, în cadrul recoltărilor multiorgan realizate de echipa de prelevare din IC Fundeni (în 2 cazuri s-a recoltat în acest bloc și ficatul). Pancreasul recoltat s-a folosit în 2 cazuri la transplantul de pancreas integral, iar in celelalte 18 cazuri, la obținerea insulelor pancreatice. Principalul rezultat a fost formarea unor echipe naționale calificate in prelevarea pancreasului și stăpânirea tehnicii de izolare a insulelor pancreatice, fapt ce reprezintă un prim pas în implementarea clinică a unui Program Național de Transplant de Insule Pancreatice. Ca implementare clinică a acestui procedeu, s-a realizat primul allotransplant de insule pancreatice din România simultan cu transplantul de ficat la un pacient în vârsta de 40 ani, cirotic, cu diabet zaharat insulino-dependent. O altă indicație a transplantului de insule pancreatice a fost managementul pancreatitei cronice. Pancreatectomia totală urmată de autotransplant de insule pancreatice reprezintă o bună opțiune în tratarea pancreatitei cronice, în special forma cu duct îngust, care chiar și cu necesarul suplimentar de insulină exogenă, asigură un control mai eficient al diabetului prin secreția de lungă durată a insulinei și peptidului C. Rezultate: În acest scop s-a realizat un autotransplant de insule pancreatice la o pacientă cu pancreatectomie totală pentru pancreatită cronică. Indicația chirurgicală de rezecție pancreatică a fost sindromul algic permanent, refractar la antalgice majore si episoadele de pancreatită acută recurente. Concluzii: Rezultatele acestui studiu sunt promiţătoare şi situează şi România pe harta ţărilor care au ca preocupare folosirea transplantului de insule pancreatice în managementul diabetului zaharat şi al pancreatitei cronice.Background: Diabetes mellitus is a global health problem, primarily due to the large number of patients (it is estimated that 20% of patients in 2015, 1 out of 11 adults were diabetic, with one out of 10 adults being diabetic by 2040); secondly, diabetes mortality outweighs the overall mortality rate through diseases such as malaria, HIV / AIDS and tuberculosis; Last but not least, the health care costs for a diabetic person are 2.3 times higher than for a non-diabetic person. Transplantation of pancreatic islets as a therapy in diabetes is a safe and effective method involving relatively easy surgery with low morbidity and mortality close to 0, compared to full pancreas transplantation. The results depend, however, on the isolating process of the pancreatic islands, a complex process that involves high costs. Methods and materials: Between 2007-2012, there were 20 harvests in the spleno-pancreatic-duodenal block, during the multiorgan harvests made by the sampling team from IC Fundeni (in 2 cases it was harvested in this block and the liver). The harvested pancreas was used in 2 cases for whole pancreas transplantation, and in the other 18 cases, the pancreatic islets were obtained. The main result was the formation of qualified national teams in pancreas extraction and the isolation of pancreatic islands, which is a first step in the clinical implementation of a National Pancreatic Transplantation Program. As a clinical implementation of this procedure, the first allotransplant of pancreatic islets in Romania was performed simultaneously with liver transplantation in a 40 year old, cirrhotic, insulin-dependent diabetes mellitus. Another indication of pancreatic islet transplantation was the management of chronic pancreatitis. Total pancreatectomy followed by pancreatic islet transplantation is a good option in the treatment of chronic pancreatitis, particularly narrow-duct form, which even with the extra exogenous insulin requirement, provides more efficient control of diabetes by long-term secretion of insulin and peptide C. Results: For this purpose a pancreatic islet transplant was performed in a patient with total pancreatectomy for chronic pancreatitis. The surgical indication of pancreatic resection was permanent algic syndrome, refractory to major antalgics, and recurrent acute pancreatitis episodes. Conclusion: The results of this study are promising and places Romania on the map of countries that are concerned with the use of pancreatic islet transplantation in the management of diabetes mellitus and chronic pancreatitis

Weak formulation for singular diffusion equation with dynamic boundary condition

In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a governing convex energy. Under suitable assumptions, the principal results of this study are stated in forms of Main Theorems A and B, which are respectively to verify: the adequacy of the weak formulation; the common property between the weak solutions and those in regular problems of standard PDEs.Comment: 23 page

On a Stochastic Wave Equation Driven by a Non-Gaussian Levy Process

This paper investigates a damped stochastic wave equation driven by a non-Gaussian Levy noise. The weak solution is proved to exist and be unique. Moreover we show the existence of a unique invariant measure associated with the transition semigroup under mild conditions.Comment: 17 page