Search results for "Boundary value problem"
showing 10 items of 551 documents
Theoretical study of a Bénard Marangoni problem
2011
[EN] In this paper we prove the existence of strong solutions for the stationary Benard-Marangoni problem in a finite domain flat on the top, bifurcating from the basic heat conductive state. The Benard-Marangoni problem is a physical phenomenon of thermal convection in which the effects of buoyancy and surface tension are taken into account. This problem is modelled with a system of partial differential equations of the type Navier-Stokes and heat equation. The boundary conditions include crossed boundary conditions involving tangential derivatives of the temperature and normal derivatives of the velocity field. To define tangential derivatives at the boundary, intended in the trace sense,…
Two -methods to generate Bézier surfaces from the boundary
2009
Two methods to generate tensor-product Bezier surface patches from their boundary curves and with tangent conditions along them are presented. The first one is based on the tetraharmonic equation: we show the existence and uniqueness of the solution of @D^4x->=0 with prescribed boundary and adjacent to the boundary control points of a nxn Bezier surface. The second one is based on the nonhomogeneous biharmonic equation @D^2x->=p, where p could be understood as a vectorial load adapted to the C^1-boundary conditions.
Basic Notions of the Theory of Heat
2016
This chapter summarizes some basic notions of thermodynamics and defines the empirical variables which are needed for the description of thermodynamic systems in equilibrium. Empirical temperature and several scales used to measure temperature are defined. The so-called “zeroth law of thermodynamics” is formulated which says that systems which are in mutual equilibrium have the same temperature. Thermodynamic ensembles corresponding to different macroscopic boundary conditions are introduced and are illustrated by simple models such as the ideal gas. Also, entropy appears on the scene for a first time, both in its statistical and its thermodynamical interpretation. Gibb’s fundamental form i…
Anomalous size-dependence of interfacial profiles between coexisting phases of polymer mixtures in thin-film geometry: A Monte Carlo simulation
1997
The interfacial profile between coexisting phases of a binary mixture (A,B) in a thin film of thickness D and lateral linear dimensions L depends sensitively on both linear dimensions and on the nature of boundary conditions and statistical ensembles applied. These phenomena generic for systems in confined geometry are demonstrated by Monte-Carlo simulations of the bond fluctuation model of symmetric polymer mixtures. Both the canonical and semi-grand-canonical ensemble are studied. In the canonical ensemble, the interfacial width w increases (from small values which are of the same order as the intrinsic profile) like sqrt{D}, before a crossover to a saturation value w_max (w_max^2 proport…
Der O2-Austausch zwischen Capillaren und Gewebe I. O2-Konzentrationsprofile in Blutcapillaren und deren Umgebung
1968
The differential equations valid for technical heat exchangers can also describe the O2 exchange in the blood capillaries and the exchange of molecules like THO and acetamid in the renal tubules. Differences in the boundary conditions occur, however. Hence, these differential equations were resolved for the corresponding boundary conditions. The results permit us to conclude that the concentration profiles occurring in the capillaries and renal tubules, as a result of diffusion in the capillary cross-section, can, generally speaking, be disregarded for the following reason: Although the differences in partial pressure between the capillary wall and capillary centre, at the beginning of the …
A model of capillary phenomena in RN with subcritical growth
2020
This paper deals with the nonlinear Dirichlet problem of capillary phenomena involving an equation driven by the p-Laplacian-like di¤erential operator in RN. We prove the existence of at least one nontrivial nonnegative weak solution, when the reaction term satisfies a sub-critical growth condition and the potential term has certain regularities. We apply the energy functional method and weaker compactness conditions.
Infinitely many solutions to boundary value problem for fractional differential equations
2018
Variational methods and critical point theorems are used to discuss existence of infinitely many solutions to boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. An example is given to illustrate our result.
The Cauchy problem in hybrid metric-Palatini f(X)-gravity
2013
The well-formulation and the well-posedness of the Cauchy problem is discussed for {\it hybrid metric-Palatini gravity}, a recently proposed modified gravitational theory consisting of adding to the Einstein-Hilbert Lagrangian an $f(R)$ term constructed {\it \`{a} la} Palatini. The theory can be recast as a scalar-tensor one predicting the existence of a light long-range scalar field that evades the local Solar System tests and is able to modify galactic and cosmological dynamics, leading to the late-time cosmic acceleration. In this work, adopting generalized harmonic coordinates, we show that the initial value problem can always be {\it well-formulated} and, furthermore, can be {\it well-…
Explicit solutions for a system of coupled Lyapunov differential matrix equations
1987
This paper is concerned with the problem of obtaining explicit expressions of solutions of a system of coupled Lyapunov matrix differential equations of the typewhere Fi, Ai(t), Bi(t), Ci(t) and Dij(t) are m×m complex matrices (members of ℂm×m), for 1≦i, j≦N, and t in the interval [a,b]. When the coefficient matrices of (1.1) are timeinvariant, Dij are scalar multiples of the identity matrix of the type Dij=dijI, where dij are real positive numbers, for 1≦i, j≦N Ci, is the transposed matrix of Bi and Fi = 0, for 1≦i≦N, the Cauchy problem (1.1) arises in control theory of continuous-time jump linear quadratic systems [9–11]. Algorithms for solving the above particular case can be found in [1…
Boundary value steady solutions of a class of hydrodynamic models for vehicular traffic flow
2003
This paper deals with the solution of a boundary value problem related to a steady nonuniform description of a class of traffic flow models. The models are obtained by the closure of the mass conservation equation with a phenomenological relation linking the local mass velocity to the local density. The analysis is addressed to define the proper framework toward the identification of the parameter characterizing the model. The last part of the paper develops a critical analysis also addressed to the design of new traffic flow models.