Search results for "Partial differential equation"
showing 10 items of 326 documents
Derivation of a Homogenized Two-Temperature Model from the Heat Equation
2014
This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential equations governing the evolution of the temperature of each phase at a macroscopic level of description. The coupling terms describing the exchange of heat between the phases are obtained by using homogenization techniques originating from [D. Cioranescu, F. Murat: Coll\`ege de France Seminar vol. 2. (Paris 1979-1980) Res. Notes in Math. vol. 60, pp. 98-138. Pitman, Boston, London, 1982.]
Elliptic equations and maps of bounded length distortion
1988
On considere l'equation elliptique d'ordre 2: L(u)=Σ i,f=1 n ∂ 1 (a ij ∂ ju )=0 ou les coefficients a ij sont des fonctions C 1 dans un domaine D de R n
On the solution of a parabolic PDE involving a gas flow through a semi-infinite porous medium
2021
Abstract Taking as start point the parabolic partial differential equation with the respective initial and boundary conditions, the present research focuses onto the flow of a sample of waste-water derived from a standard/conventional dyeing process. In terms of a highly prioritized concern, meaning environment decontamination and protection, in order to remove the dyes from the waste waters, photocatalyses like ZnO or TiO2 nanoparticles were formulated, due to their high surface energy which makes them extremely reactive and attractive. According to the basics of ideal fluid, the key point is the gas flow through an ideal porous pipe consisting of nanoparticles bound one to each other, for…
Accounting for preferential sampling in species distribution models
2019
D. C., A. L. Q. and F. M. would like to thank the Ministerio de Educación y Ciencia (Spain) for financial support (jointly financed by the European Regional Development Fund) via Research Grants MTM2013‐42323‐P and MTM2016‐77501‐P, and ACOMP/2015/202 from Generalitat Valenciana (Spain). Species distribution models (SDMs) are now being widely used in ecology for management and conservation purposes across terrestrial, freshwater, and marine realms. The increasing interest in SDMs has drawn the attention of ecologists to spatial models and, in particular, to geostatistical models, which are used to associate observations of species occurrence or abundance with environmental covariates in a fi…
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.
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…
Gradient flows in random walk spaces
2021
El món digital ha comportat l'aparició de molts tipus de dades, de mida i complexitat creixents. De fet, els dispositius moderns ens permeten obtenir fàcilment imatges de major resolució, així com recopilar dades sobre cerques a la xarxa, anàlisis sanitàries, xarxes socials, sistemes d'informació geogràfica, etc. En conseqüència, l'estudi i el tractament d'aquests grans conjunts de dades té un gran interès i valor. En aquest sentit, els grafs ponderats proporcionen un espai de treball natural i flexible on representar les dades. En aquest context, un vèrtex representa una dada concreta i a cada aresta se li assigna un pes segons alguna mesura de semblança adequadament triada entre els vèrte…
A tribute to Massimo Lanza de Cristoforis
2020
It is with great pleasure that we dedicate the special issue Functional Analytic Methods in Partial Differential Equations of Complex Variables and Elliptic Equations to the 60th birthday of Massim...
From the Big Five to the General Factor of Personality: a Dynamic Approach
2014
AbstractAn integrating and dynamic model of personality that allows predicting the response of the basic factors of personality, such as the Big Five Factors (B5F) or the general factor of personality (GFP) to acute doses of drug is presented in this paper. Personality has a dynamic nature, i.e., as a consequence of a stimulus, the GFP dynamics as well as each one of the B5F of personality dynamics can be explained by the same model (a system of three coupled differential equations). From this invariance hypothesis, a partial differential equation, whose solution relates the GFP with each one of the B5F, is deduced. From this dynamic approach, a co-evolution of the GFP and each one of the B…
On stability issues for IMEX schemes applied to 1D scalar hyperbolic equations with stiff reaction terms
2011
The application of a Method of Lines to a hyperbolic PDE with source terms gives rise to a system of ODEs containing terms that may have very different stiffness properties. In this case, Implicit-Explicit Runge-Kutta (IMEX-RK) schemes are particularly useful as high order time integrators because they allow an explicit handling of the convective terms, which can be discretized using the highly developed shock capturing technology, together with an implicit treatment of the source terms, necessary for stability reasons. Motivated by the structure of the source term in a model problem introduced by LeVeque and Yee in [J. Comput. Phys. 86 (1990)], in this paper we study the preservation of ce…