optimal system invariant solutions and evolution of weak discontinuity for isentropic drift flux model abstract inequivalent classes of similarity solutions for isentropic drift flux two phase flow model are obtained by using one dimensional optimal classifications the optimality of this classification is shown in a constructive manner i e by constructing various invariant functions including conditional and numerical invariants further with the help of invariant solution we discuss the evolution of weak discontinuity which displays the nature of the general solution

lie symmetry classification analysis for nonlinear coupled diffusion the group properties of the 1 1 dimensional matrix diffusion equation of the form with respect to point symmetries are given it is shown that in particular cases the group properties of this equation are similar to those of the corresponding scalar equation namely the lie algebra is extended for power and exponential functions with additional extensions when powers of and 2 exist however a specific form of is shown to exist for cases admitting both infinite and finite groups the result obtained is used to construct new group invariant solutions for impulsive boundary inputs using two similarity variables a reduction is applied to the coupled diffusion of temperature and volumetric moisture content in porous media under periodic boundary conditions a perturbation method is employed to obtain an explicit solution for the case when can be expressed exponentially in terms of the similarity variables

potential symmetries of nonlinear diffusion convection equations in this paper potential symmetries are sought for the nonlinear diffusion convection equations the functional forms of f u and k u that admit such symmetries are completely classified

exact polynomial solutions to some nonlinear diffusion equations abstract a class of non group invariant exact solutions to a number of nonlinear diffusion equations is constructed expressed in the appropriate variables these solutions are polynomials in the spatial variable the method is mainly applicable to equations which may be written in an appropriate quadratically nonlinear form a number of equivalence transformations between various nonlinear diffusion equations are also derived

potential symmetries of a porous medium equation potential symmetries which are not local symmetries are carried out for the porous medium equation where when it can be written in a conserved form these symmetries are realized as local symmetries of a related auxiliary system and lead to the construction of corresponding invariant solutions as well as to the linearization of the equation by non invertible mappings

new non lie ansatze and exact solutions of nonlinear reaction diffusion convection equations a constructive method for obtaining new exact solutions of nonlinear evolution equations is further developed the method is based on the consideration of a fixed nonlinear partial differential equation together with an additional generating condition in the form of a linear high order ordinary differential equation using this method new non lie ansatze and exact solutions are obtained for two classes of diffusion equations with power and exponential nonlinearities which describe real processes in physics chemistry and biology the analysis of the found solutions and the relation of the proposed method to some approaches which have been suggested in several recently published papers are presented

global identification of risk preferences with revealed preference data abstract the concept of parameter identification for a given specification is differentiated from global identification which specification is right first order conditions for production under risk are shown to admit many alternative specification pairs representing risk preferences and either perceived price risk production risk or the deterministic production structure imposing an arbitrary specification on any of the latter three determines which risk preference specification fits a given dataset undermining global identification even when parameter identification is suggested by typical statistics this lack of identification is not relaxed by increasing the number of observations critical implications for estimation of mean variance specifications are derived

two dimensional symmetry reduction of 2 1 dimensional nonlinear klein gordon equation in this paper one dimensional optimal system of group invariant solutions of 2 1 dimensional klein gordon system is constructed then the classification of group invariant solutions is given out and the corresponding two dimensional symmetry reduced equations are obtained at last some symmetry transformations are gained in detail especially we obtain the most general solution from a given solution by use of six variable one parameter subgroups transformations

group classification for isothermal drift flux model of two phase flows in this paper a full symmetry group classification for isothermal multiphase drift flux model is presented all invariant functions are developed for the lie algebra which play a vital role in construction of optimal systems further with the help of one dimensional optimal classification group invariant solutions are obtained which describe the asymptotic behavior of general solution

a note on optimal systems for the heat equation a rigorous proof of the optimality of one to five parameter systems for the symmetry group of the one dimensional heat equation is given

exact results for the nonlinear diffusion equations delta u delta t delta delta x u 4 3 delta u delta x and delta u delta t delta delta x u 2 3 delta u delta x the author exploits local and non local symmetries of the two equations of the title and of some related equations some new exact solutions are derived and some specific boundary value problems of physical significance are considered

optimal system symmetry reductions and new closed form solutions for the geometric average asian options in this paper the lie group analysis method is applied to the geometric average asian option pricing equation in financial problems firstly the complete lie symmetry group and infinitesimal generators of this equation are derived then the optimal system with one parameter for the lie symmetry algebra are obtained which gives the possibility to describe a complete set of invariant solutions to the pricing equation finally based on the optimal system the symmetry reductions and corresponding closed form solutions for the pricing equation are proposed

group transformations and the nonlinear heat diffusion equation a nonlinear diffusion equation with a power law diffusion coefficient is studied self similar and partially invariant solutions are shown to be identical the theory of homology is introduced and used to generate classes of equations the solutions of which are related through backlund transformations an example of an application is given which generalizes the solution of storm j appl phys 22 1951 pp 940 951 on heat conduction in metals

constructing two dimensional optimal system of the group invariant solutions to search for inequivalent group invariant solutions of two dimensional optimal system a direct and systematic approach is established which is based on commutator relations adjoint matrix and the invariants the details of computing all the invariants for two dimensional algebra are presented which is shown more complex than that of one dimensional algebra the optimality of two dimensional optimal systems is shown clearly for each step of the algorithm with no further proof to leave the algorithm clear each stage is illustrated with a couple of examples the heat equation and the novikov equation finally two dimensional optimal system of the 2 1 dimensional navier stokes ns equation is found and used to generate intrinsically different reduced ordinary differential equations some interesting explicit solutions of the ns equation are provided

potential symmetries and new solutions of a simplified model for reacting mixtures in this paper we investigate potential symmetries of a simplified model for reacting mixtures we find new similarity reductions and wider class of solutions through this approach further we explore an invertible mapping which linearizes the reacting mixture model

potential symmetries to systems of nonlinear diffusion equations in this paper the potential symmetry method is developed to study systems of nonlinear diffusion equations potential variables of the systems are introduced through conservation laws such conservation laws yield equivalent systems auxiliary systems of pdes with the given dependent and potential variables as new dependent variables lie point symmetries of the auxiliary systems which cannot be projected to the vector fields of the given dependent and independent variables yield potential symmetries of the systems classification for systems of nonlinear diffusion equations with two and three components is performed symmetry reductions associated with the potential symmetries are presented

symmetry reductions and exact solutions of the affine heat equation lie symmetry group method is applied to study the affine heat equation for surface its symmetry groups and corresponding optimal systems are determined and group invariant solutions associated to the symmetries are obtained and classified

mathematical simulation of osteotomy numerical analysis and results abstract in this paper a model problem of one vital surgical technique in orthopaedics the so called osteotomy will be analyzed numerically the model problem will be formulated mathematically the problem leads to solving the variational equality and inequality the finite element method will be used in numerical solution and the algorithm will be given

instrumental variable estimator for the nonlinear errors in variables model abstract estimation for the nonlinear errors in variables model is considered it isassumed that additional information is available in the form of observations on instrumental variables an estimation procedure is presented for the parameters of the model asymptotic properties of the estimator are investigated

homogeneous diffusion in ℝ with power like nonlinear diffusivity we study the nonnegative solutions of the initial value problem ut ur ux p 1ux x u x 0 l1 where p 0 r p 0 the local velocity of propagation of the solutions is identified as v vx vx p 1 where v cu with r p 1 p and c r p r p 1 is the nonlinear potential our main result is the a priori estimate vx vx p 1 x frac 1 2p r t

investigating generalisations of expected utility theory using experimental data a number of generalizations of the expected utility preference functional are estimated using experimentally generated data involving 100 pairwise choice questions repeated on two separate occasions likelihood ratio tests are conducted to investigate the statistical superiority of the various generalizations and the akaike information criterion is used to distinguish between them the economic superiority of the various generalizations is also explored and the paper concludes that for many subjects the superiority of several of the generalizations is not established copyright 1994 by the econometric society

homology and the nonlinear heat diffusion equation the concept of homology siam j appl math 40 1981 pp 191 207 is generalized to an arbitrary nonlinear diffusion equation a large class of self homologous diffusion coefficients is introduced and used to examine possible changes in initial and boundary conditions through homologous transformations generalized homology is shown to be identical to backlund transformations

group theoretical framework for potential symmetries of evolution equations we develop algebraic approach to the problem of classification of potential symmetries of nonlinear evolution equations it is essentially based on the recently discovered fact r zhdanov j math phys 50 053522 2009 that any such symmetry is mapped into a contact symmetry the approach enables using the classical results on classification of contact symmetries of nonlinear evolution equations by sokolov and magadeev to classify evolution equations admitting potential symmetries we construct several examples of new nonlinear fourth order evolution equations admitting potential symmetries since the symmetries obtained depend on nonlocal variables they cannot be derived by the infinitesimal lie approach

new classes of symmetries for partial differential equations new classes of symmetries for partial differential equations are introduced by writing a given partial differential equation s in a conserved form a related system t with potentials as additional dependent variables is obtained the lie group of point transformations admitted by t induces a symmetry group of s new symmetries may be obtained for s that are neither point nor lie backlund symmetries they are determined by a completely algorithmic procedure significant new symmetries are found for the wave equation with a variable wave speed and the nonlinear diffusion equation

symmetry groups and separation of variables of a class of nonlinear diffusion convection equations in this paper a class of nonlinear diffusion convection equations ut d u uxn x p u ux which has quite a large number of physical applications is analysed by using symmetry group methods which include the classical method the potential symmetry method and the generalized conditional symmetry method a complete classification of the functional forms of the diffusion and convection coefficients is presented when the equation admits lie s point symmetry groups and potential symmetry groups the separation of variables for the equation is investigated using the generalized conditional symmetry approach for some interesting cases exact solutions using the method of separation of variables are discussed in detail

the use of lie transformation groups in the solution of the coupled diffusion equation the solutions of coupled linear and nonlinear diffusion equations in a semi infinite medium are derived using the method of continuous one parameter point symmetry group invariants initially conditions for both classical and non classical lie group invariants are developed and solutions are derived corresponding to linear coupled diffusion the non classical invariants are shown to be expressible in terms of a linear parabolic operator in addition solutions corresponding to constant impulse and sinusoidally time varying condition are derived from the equations determining classical group invariance nonlinear cases are also considered the classical symmetry groups for any form of diffusion matrix are presented in addition the point source solution for a power law form governing the diffusion matrix is derived it is a natural extension of the scalar analogue

production function estimation reviving the primal much of the discussion on the estimation of production functions is related to the fact that inputs may be endogenous and therefore direct estimators of the production functions may be inconsistent one way to overcome this problem has been to apply the concept of duality the purpose of this note is to point out that estimates based on duality unlike direct estimators of the production function do not utilize all the available information and therefore are statistically inefficient and the loss in efficiency may be sizeable examination of the sources of input variability suggests generalizations of currently used estimators a simple model duality theory is a microtheory and as such its empirical implications are related to firm rather than market data our discussion is conducted within this framework and we ignore further complications that arise from the use of aggregate market data the conceptual problems in the choice of estimators can be presented in terms of a well known simple model whatever other virtues more complex models possess the problems discussed here are not resolved by the added complexity let the production function be

parabolic equations for curves on surfaces part i curves with p integrable curvature this is the first of a two part paper in which we develop a theory of parabolic equations for curves on surfaces which can be applied to the so called curve shortening of flow by mean curvature problem as well as to a number of models for phase transitions in two dimensions we introduce a class of equations for which the initial value problem is solvable for initial data with p integrable curvature and we also give estimates for the rate at which the p norms of the curvature must blow up if the curve becomes singular in finite time a detailed discussion of the way in which solutions can become singular and a method for continuing the solution through a singularity will be the subject of the second part

a direct algorithm of one dimensional optimal system for the group invariant solutions a direct and systematic algorithm is proposed to find one dimensional optimal system for the group invariant solutions which is attributed to the classification of its corresponding one dimensional lie algebra since the method is based on different values of all the invariants the process itself can both guarantee the comprehensiveness and demonstrate the inequivalence of the optimal system with no further proof to leave the algorithm clear we illustrate each stage with a couple of well known examples the korteweg de vries equation and the heat equation finally we apply our method to the novikov equation and use the found optimal system to investigate the corresponding invariant solutions

the heat equation shrinking convex plane curves soient m et m des varietes de riemann et f m m une application reguliere si m est une courbe convexe plongee dans le plan r 2 l equation de la chaleur contracte m a un point

painleve analysis auto backlund transformations and exact solutions for a simplified model for reacting mixtures abstract recently a simplified model for reacting mixtures was investigated to admit the potential symmetries only when the structure function f u in the model was of the form u 2 k in this paper we investigate some other properties of the nonlinear model with the condition f u u 2 k firstly the painleve analysis is performed such that it is shown that this equation passes the painleve test and then two new types of auto backlund transformations abts are found by using the truncated painleve expansion analysis and some ansatz the abts reduce the nonlinear model to the systems of linear partial differential equations with respect to the new introduced variables finally based on the obtained auto backlund transformations we explore some explicit exact solutions including soliton solutions singular soliton solutions soliton like solutions rational solutions and other types of solutions which may be useful to explain the corresponding physical phenomena

some non local transformations between nonlinear diffusion equations generalized backlund transformations are applied to derive links between a large number of different types of nonlinear diffusion equations including many which are of physical significance some new exactly linearizable forms are determined

numerical solution of the contact problem application to a simple model of the human hip joint abstract we draw on the mathematical formulation of the contact problem which leads to the variational inequality fem is used for discretization the variational inequality enables additional contact elements to be avoided where a suitable stiffness parameter is needed moreover we obtain the asymptotic estimate model of a human hip joint is analysed in the application this analysis may be useful for modelling the human hip joint replacement after surgical reconstruction of the dysplastic acetabulum

lie transformations nonlinear evolution equations and painleve forms we present the results of a systematic investigation of invariance properties of a large class of nonlinear evolution equations under a one parameter continuous lie group of transformations it is shown that in general the corresponding invariant variables the subclass of which is the usual similarity variables lead to ordinary differential equations of painleve type in the case of inverse scattering transform solvable equations as conjectured by ablowitz ramani and segur this is found to be also true for certain higher spatial dimensional versions such as the kadomtsev petviashivilli two dimensional sine gordon and ernst equations for the nonsolvable equations considered here this invariance study leads to ordinary differential equations with movable critical points

group invariant solutions and optimal systems for multidimensional hydrodynamics the group properties of the three dimensional 3 d one temperature hydrodynamic equations including nonlinear conduction and a thermal source are presented a subgroup corresponding to axisymmetric geometry is chosen and the details of the construction of the one and two dimensional optimal systems are shown the two dimensional optimal system is used to generate 23 intrinsically different reductions of the 2 d partial differential equations to ordinary differential equations these ordinary differential equations can be solved to provide analytic solutions to the original partial differential equations two example analytic solutions are presented a 2 d axisymmetric flow with a p2 asymmetry and a 3 d spiraling flow

on the exactly solvable equation s_t beta s gamma 2 s_x _x alpha beta s gamma 2 s_x occurring in two phase flow in porous media the symmetry approach of fokas j math phys 21 1980 pp 1318 1325 is used to show that the most general equation of the form s t g s s xx f s s x dg ds ne 0 which is exactly solvable is equivalent to the equation s t beta s gamma 2 s x x alpha beta s gamma 2 s x this equation is then mapped to the linear heat equation through a series of backlund transformations the above result is used to solve an initial boundary value problem modeling the process of waterflooding i e the displacement of oil initially in a porous reservoir by continuously injected water

finite element analysis of contact problems in thermoelasticity the semi coercive case abstract numerical analysis of the signorini problem with friction in two dimensional quasi coupled linear thermoelasticity is investigated piecewise linear finite elements on the triangulation of the given domain r 2 with polygonal boundary are used in this contribution we establish the rate of convergence of the finite element approximate solution u h provided the exact solution is smooth enough in general the problem represents the model problem of a great number of branches such as the model problem of a high level radioactive waste disposal system as well as the model problem of geodynamcis and biomechanics etc