Search results for "gradient"
showing 10 items of 725 documents
Fluid reservoirs in the crust and mechanical coupling between the upper and lower crust
2004
An important observation associated with seismic activity on the Nagamachi-Rifu Fault is the existence of tabular, fluid rich zones at mid-crustal levels. These zones resemble the “bright spots” seen in many seismic images of the crust worldwide. The aim of this paper is to develop the mechanical foundations for the formation of such zones. To do so requires an understanding of the distribution of pore fluid pressure in a deforming crust. In a hydrostatically stressed porous material, the pore fluid pressure should equal the mean stress in order to keep the pores from collapsing. Past discussions of this subject imply very high pore fluid pressures, two to three times lithostatic. Considera…
Existence and asymptotic properties for quasilinear elliptic equations with gradient dependence
2016
Abstract The paper focuses on a Dirichlet problem driven by the ( p , q ) -Laplacian containing a parameter μ > 0 in the principal part of the elliptic equation and a (convection) term fully depending on the solution and its gradient. Existence of solutions, uniqueness, a priori estimates, and asymptotic properties as μ → 0 and μ → ∞ are established under suitable conditions.
Multiple solutions for a Dirichlet problem with p-Laplacian and set-valued nonlinearity
2008
AbstractThe existence of a negative solution, of a positive solution, and of a sign-changing solution to a Dirichlet eigenvalue problem with p-Laplacian and multi-valued nonlinearity is investigated via sub- and supersolution methods as well as variational techniques for nonsmooth functions.
Elliptic problems with convection terms in Orlicz spaces
2021
Abstract The existence of a solution to a Dirichlet problem, for a class of nonlinear elliptic equations, with a convection term, is established. The main novelties of the paper stand on general growth conditions on the gradient variable, and on minimal assumptions on Ω. The approach is based on the method of sub and supersolutions. The solution is a zero of an auxiliary pseudomonotone operator build via truncation techniques. We present also some examples in which we highlight the generality of our growth conditions.
Nonlinear elliptic equations having a gradient term with natural growth
2006
Abstract In this paper, we study a class of nonlinear elliptic Dirichlet problems whose simplest model example is: (1) { − Δ p u = g ( u ) | ∇ u | p + f , in Ω , u = 0 , on ∂ Ω . Here Ω is a bounded open set in R N ( N ⩾ 2 ), Δ p denotes the so-called p-Laplace operator ( p > 1 ) and g is a continuous real function. Given f ∈ L m ( Ω ) ( m > 1 ), we study under which growth conditions on g problem (1) admits a solution. If m ⩾ N / p , we prove that there exists a solution under assumption (3) (see below), and that it is bounded when m > N p ; while if 1 m N / p and g satisfies the condition (4) below, we prove the existence of an unbounded generalized solution. Note that no smallness condit…
Elliptic equations having a singular quadratic gradient term and a changing sign datum
2012
In this paper we study a singular elliptic problem whose model is \begin{eqnarray*} - \Delta u= \frac{|\nabla u|^2}{|u|^\theta}+f(x), in \Omega\\ u = 0, on \partial \Omega; \end{eqnarray*} where $\theta\in (0,1)$ and $f \in L^m (\Omega)$, with $m\geq \frac{N}{2}$. We do not assume any sign condition on the lower order term, nor assume the datum $f$ has a constant sign. We carefully define the meaning of solution to this problem giving sense to the gradient term where $u=0$, and prove the existence of such a solution. We also discuss related questions as the existence of solutions when the datum $f$ is less regular or the boundedness of the solutions when the datum $f \in L^m (\Omega)$ with …
Existence and comparison results for a singular semilinear elliptic equation with a lower order term
2014
This paper deals with the homogeneous Dirichlet problem for a singular semilinear elliptic equation with a first order term. When the datum is bounded we prove an existence result and we show that any solution can be compared with the solution to a suitable symmetrized problem.
Cores for parabolic operators with unbounded coefficients
2009
Abstract Let A = ∑ i , j = 1 N q i j ( s , x ) D i j + ∑ i = 1 N b i ( s , x ) D i be a family of elliptic differential operators with unbounded coefficients defined in R N + 1 . In [M. Kunze, L. Lorenzi, A. Lunardi, Nonautonomous Kolmogorov parabolic equations with unbounded coefficients, Trans. Amer. Math. Soc., in press], under suitable assumptions, it has been proved that the operator G : = A − D s generates a semigroup of positive contractions ( T p ( t ) ) in L p ( R N + 1 , ν ) for every 1 ⩽ p + ∞ , where ν is an infinitesimally invariant measure of ( T p ( t ) ) . Here, under some additional conditions on the growth of the coefficients of A , which cover also some growths with an ex…
From the Golgi-Cajal mapping to the transmitter-based characterization of the neuronal networks leading to two modes of brain communication: Wiring a…
2007
After Golgi-Cajal mapped neural circuits, the discovery and mapping of the central monoamine neurons opened up for a new understanding of interneuronal communication by indicating that another form of communication exists. For instance, it was found that dopamine may be released as a prolactin inhibitory factor from the median eminence, indicating an alternative mode of dopamine communication in the brain. Subsequently, the analysis of the locus coeruleus noradrenaline neurons demonstrated a novel type of lower brainstem neuron that monosynaptically and globally innervated the entire CNS. Furthermore, the ascending raphe serotonin neuron systems were found to globally innervate the forebrai…
Column-switching techniques for screening of diuretics and probenecid in urine samples
1994
A method based on high-performance liquid chromatography using column-switching is described for the screening of diuretics and probenecid in urine samples. The system uses a 20- x 2.1-mm i.d. precolumn, packed with a Hypersil ODS-C18, 30-microns stationary phase, for the on-line sample cleanup and enrichment. Untreated urine samples are directly injected, and the precolumn is flushed for 1 min with water to eliminate polar matrix components. The retained analytes are then back-flushed by means of a six-port switching valve onto a Hypersil ODS-C18 analytical column (5 microns, 250- x 4-mm i.d.), where they are separated using an acetonitrile/phosphate buffer (pH = 3) gradient elution. Under…