Search results for "PDE"
showing 10 items of 558 documents
A continuous time tug-of-war game for parabolic $p(x,t)$-Laplace type equations
2019
We formulate a stochastic differential game in continuous time that represents the unique viscosity solution to a terminal value problem for a parabolic partial differential equation involving the normalized $p(x,t)$-Laplace operator. Our game is formulated in a way that covers the full range $1<p(x,t)<\infty$. Furthermore, we prove the uniqueness of viscosity solutions to our equation in the whole space under suitable assumptions.
Sharp capacity estimates for annuli in weighted R^n and in metric spaces
2017
We obtain estimates for the nonlinear variational capacity of annuli in weighted R^n and in metric spaces. We introduce four different (pointwise) exponent sets, show that they all play fundamental roles for capacity estimates, and also demonstrate that whether an end point of an exponent set is attained or not is important. As a consequence of our estimates we obtain, for instance, criteria for points to have zero (resp. positive) capacity. Our discussion holds in rather general metric spaces, including Carnot groups and many manifolds, but it is just as relevant on weighted R^n. Indeed, to illustrate the sharpness of our estimates, we give several examples of radially weighted R^n, which …
Minimality via second variation for microphase separation of diblock copolymer melts
2017
Abstract We consider a non-local isoperimetric problem arising as the sharp interface limit of the Ohta–Kawasaki free energy introduced to model microphase separation of diblock copolymers. We perform a second order variational analysis that allows us to provide a quantitative second order minimality condition. We show that critical configurations with positive second variation are indeed strict local minimizers of the problem. Moreover, we provide, via a suitable quantitative inequality of isoperimetric type, an estimate of the deviation from minimality for configurations close to the minimum in the L 1 {L^{1}} -topology.
Non-autonomous rough semilinear PDEs and the multiplicative Sewing Lemma
2021
We investigate existence, uniqueness and regularity for local solutions of rough parabolic equations with subcritical noise of the form $du_t- L_tu_tdt= N(u_t)dt + \sum_{i = 1}^dF_i(u_t)d\mathbf X^i_t$ where $(L_t)_{t\in[0,T]}$ is a time-dependent family of unbounded operators acting on some scale of Banach spaces, while $\mathbf X\equiv(X,\mathbb X)$ is a two-step (non-necessarily geometric) rough path of H\"older regularity $\gamma >1/3.$ Besides dealing with non-autonomous evolution equations, our results also allow for unbounded operations in the noise term (up to some critical loss of regularity depending on that of the rough path $\mathbf X$). As a technical tool, we introduce a versi…
Sāpju vadīšana pediatriskiem pacientiem apdeguma gadījumā
2019
Bakalaura darba tēma – Sāpju vadīšana pediatriskiem pacientiem apdegumu gadījumā. Šī tēma ir aktuāla, jo statistika liecina, ka katru gadu bērnu apdegumu skaits arvien pieaug. Salīdzinot 2016. gada un 2017. gada datus, apdegumu skaits bērnu vidu pieaudzis par septiņiem gadījumiem. Lielākā riska grupa apdegumu traumām ir bērni vecuma posmā no trīs gadu vecuma, kas applaucējumus vairumā iegūst vecāku neuzmanības dēļ. Darba izstrādāšanas mērķis – Noskaidrot sāpju vadīšanas principus pediatriskiem pacientiem apdegumu gadījumā. Darba uzdevumi ir izanalizēt un apkopot iegūtos datus par sāpju vadīšanas principiem pediatriskiem pacientiem apdegumu gadījumā. Analizēt Virdžīnijas Hendersones māszinīb…
β-Adrenoceptor stimulation up-regulates phosphodiesterase 4 activity and reduces prostaglandin E 2 -inhibitory effects in human neutrophils
2000
Human neutrophils were treated for 4 h with a combination of salbutamol (1 µM), a β2-adrenoceptor agonist, and rolipram (30 µM), a selective phosphodiesterase 4 inhibitor, to investigate whether this treatment produces up-regulation of phosphodiesterase activity with functional consequences. Anion-exchange chromatography coupled with the use of selective activators and inhibitors demonstrated that a phosphodiesterase activity with characteristics of the isoenzyme type 4 was increased in drug-treated cells. Kinetic analysis showed a ~1.5-fold increase in V max without alteration of K m values. The augmented phosphodiesterase activity in drug-treated cells was abolished by actinomycin D. Cycl…
Correlation of nitric oxide and atrial natriuretic peptide changes with altered cGMP homeostasis in liver cirrhosis.
2005
: Background: Cyclic GMP (cGMP) concentration is increased in plasma of patients with liver cirrhosis. Three possible mechanisms may contribute: increased cGMP synthesis by soluble (activated by nitric oxide), or particulate (activated by atrial natriuretic peptide (ANP)) guanylate cyclase or increased release from cells. Aim: The aim of this work was to analyze the possible contributors to increased plasma cGMP and to assess whether changes in the parameters of the system vary with the degree of liver disease (Child Pugh score) or by the presence of ascites. Methods: We measured cGMP in plasma and lymphocytes, soluble guanylate cyclase activation by nitric oxide in lymphocytes, nitrates an…
Effects of sildenafil on human penile blood vessels.
2000
Abstract Objectives. To investigate the effects of sildenafil on human penile blood vessels and evaluate the interaction of sildenafil with neurogenic-mediated responses. Sildenafil is currently used in the treatment of erectile dysfunction. Methods. Penile dorsal arteries and deep dorsal veins were obtained from 14 multiorgan donors. Vascular rings were suspended in organ bath chambers, and the isometric tension was recorded. We then studied the effects of sildenafil on precontracted vessels and the neurogenic (noradrenergic and nitrergic) responses. Results. Sildenafil (10 −9 to 3 × 10 −6 M) caused concentration-dependent relaxation and amplified the relaxation induced by sodium nitroprus…
Akūtas nieru mazspējas riska faktoru analīze smagas termiskas traumas slimniekiem
2022
Par spīti arvien plašākām diagnostikas, prevencijas un ārstēšanas iespējām, akūts nieru bojājums joprojām ir nozīmīga smagas termiskas traumas komplikācija ar augstu incidenci un mirstību. Darba mērķis: Identificēt riska faktorus, kas izraisa akūtu nieru mazspēju smagas apdeguma traumas pacientiem (TBSA ≥ 20%). Metodes un materiāli: Pētījums veikts RAKUS stacionāra “Biķernieki” Valsts Apdegumu centrā. Dati iegūti retrospektīvi analizējot 1997 pacientu medicīniskās slimības vēstures, laika posmā no 2011. – 2021. gadam, kas atlasītas, izmantojot SSK-10 klasifikāciju pēc koda T29 – vairāku un neprecizētu ķermeņa apvidu termiski un ķīmiski apdegumi, pētījumā iekļaujot 248 pacientus, vecumā no 1…
Supersymmetric structures for second order differential operators
2012
Necessary and sufficient conditions are obtained for a real semiclassical partial differential operator of order two to possess a supersymmetric structure. For the operator coming from a chain of oscillators, coupled to two heat baths, we show the non-existence of a smooth supersymmetric structure, for a suitable interaction potential, provided that the temperatures of the baths are different.