Search results for "Initial value problem"
showing 6 items of 96 documents
Stability of degenerate parabolic Cauchy problems
2015
We prove that solutions to Cauchy problems related to the $p$-parabolic equations are stable with respect to the nonlinearity exponent $p$. More specifically, solutions with a fixed initial trace converge in an $L^q$-space to a solution of the limit problem as $p>2$ varies.
Symmetric Galerkin BEM for Non Linear Analysis of Historical Masonries
2015
The preservation of the historical and monumental buildings, but also of the considerable heritage of old constructions made by traditional techniques, is one of the actual problems of the structural mechanics. The level of knowledge of their structural behavior in presence of external actions is made through calculus methods and simple procedures in order to allow a reading of the material suffering degree and as a consequence of the related safety. Unfortunately, often the masonry panels show openings located in an irregular way and cracks having small or big dimensions. In these cases the employment of strategies, as for example the identifying of the masonry piers and the transformation…
Rotationally symmetric 1-harmonic flows from D2 TO S 2: Local well-posedness and finite time blowup
2010
The 1-harmonic flow from the disk to the sphere with constant Dirichlet boundary conditions is analyzed in the case of rotational symmetry. Sufficient conditions on the initial datum are given, such that a unique classical solution exists for short times. Also, a sharp criterion on the boundary condition is identified, such that any classical solution will blow up in finite time. Finally, nongeneric examples of finite time blowup are exhibited for any boundary condition.
Transition dynamics in optical fiber amplifiers operating in the normal dispersion regime
2011
Over the past decade there has been large interest in ultrafast optical fiber amplifiers operating in the normal dispersion regime because of the discovery that, high-energy pulses with a parabolic intensity profile and linear frequency chirp are the asymptotic solution to the system for arbitrary initial conditions [1]. These so-called “similariton” solutions propagate in a self-similar manner, holding certain relations (scaling) between pulse power, duration, and chirp parameter. While the asymptotic similariton features seem now well understood [1], the physics of the transition to this solution from arbitrary initial pulses has not been fully explored yet (most of the previous attempts …
Age-Structured Human Population Dynamics
2006
ABSTRACT A von Foerster-McKendrick model to study age-structured human population dynamics is presented in this paper. Forecasts of population density (population per age unit) depending on ages are possible using this model. The model consists of a quasi-linear first order partial differential equation for the dynamics of population density per age-unit (except for the zero-age), a boundary condition for the births flow at zero-age, and an initial condition for the population density at the initial instant. A general solution independent of the particular human-system under study is obtained based on some hypotheses about the mathematical structure of its input variables. The model has bee…
A note on some fundamental results in complete gauge spaces and application
2015
We discuss the extension of some fundamental results in nonlinear analysis to the setting of gauge spaces. In particular, we establish Ekeland type and Caristi type results under suitable hypotheses for mappings and cyclic mappings. Our theorems generalize and complement some analogous results in the literature, also in the sense of ordered sets and oriented graphs. We apply our results to establishing the existence of solution to a second order nonlinear initial value problem.