orthogonal grid generation of an irregular region using a local polynomial collocation method abstract in this study a 2 d orthogonal grid generation model is developed by solving the governing equations of coordinate transformation with a local polynomial collocation method accompanied with the moving least squares mls approach this method was developed in a way that on the boundaries both the governing equation and boundary condition are satisfied so it is more robust and accurate than conventional collocation methods though the method used to solve the coordinate transforming equations is meshless it does not deteriorate the value of present work because most numerical models in modern use are grid dependent and grid generation of service to these models is still strongly desired particularly for finite difference models in irregular domains before applying to grid generation problems the performance of present method is tested by a bench mark potential flow problem additional to two basic grid generation problems a bottleneck problem of previous works which contains zero degree corners in the domain is carried out finally the model is applied to the orthogonal grid generation in a multi connected domain the correctness is testified by checking the orthogonality of the generated results

efficient pseudospectral flow simulations in moderately complex geometries a computationally efficient pseudospectral method is developed for incompressible flow simulations in two dimensional geometries involving periodicity in one direction and significant surface deformations a pseudoconformal mapping is used to map the flow domain into a rectangle thereby establishing an orthogonal curvilinear coordinate system within which the governing equations are formulated the time integration of the spectrally discretized two dimensional momentum equations is performed by a second order mixed explicit implicit time integration scheme the satisfaction of the continuity equation is obtained through the solution of a poisson equation for the pressure and the use of the influence matrix technique a highly efficient iterative solver has been developed for the solution of a generalized stokes problem at each time step based on a spectrally preconditioned biconjugate gradient algorithm which exhibits almost linear scalability requiring an ordernlog2nnumber of operations wherenis the number of unknowns numerical results are presented for two dimensional steady oscillatory and peristaltic flows within an undulating channel which agree well with previous results that have appeared in the literature

forward backward and symmetric stochastic integration we define three types of non causal stochastic integrals forward backward and symmetric our approach consists in approximating the integrator two optics are considered the first one is based on traditional usual stochastic calculus and the second one on wiener distributions

existence of an exact solution for a one phase stefan problem with nonlinear thermal coefficients from tirskii s method abstract the mathematical analysis of a one phase lame clapeyron stefan problem with nonlinear thermal coefficients following g a tirskii two exact solutions of stefan s nonlinear problem sov phys dokl 4 1959 288 292 is obtained two related cases are considered one of them has a temperature condition on the fixed face x 0 and the other one has a flux condition of the type q 0 t q 0 0 we obtain in both cases sufficient conditions for data in order to have the existence of an explicit solution of a similarity type which is given by using a double fixed point

a non iterative scheme for orthogonal grid generation with control function and specified boundary correspondence on three sides a new numerical scheme is proposed for generating an orthogonal grid in a simply connected 2d domain the scheme is based on the idea of decomposition of a global orthogonal transform into consecutive mappings of a conformal mapping and an auxiliary orthogonal mapping which was suggested by kang and leal j comput phys 102 78 1992 the method is non iterative and flexible in the adjustment of grid spacing the grid spacing can be controlled mainly by specification of the boundary correspondence up to three sides of the boundary the method is also equipped with a control function that provides further degrees of freedom in the grid spacing adjustment from a mathematical viewpoint the proposed scheme can also be regarded as a numerical implementation of the constructive proof for the existence of a solution of the orthogonal mapping problem in an arbitrary simply connected domain under the condition that the boundary correspondence is specified on three sides

explicit solution for a stefan problem with variable latent heat and constant heat flux boundary conditions abstract in voller swenson and paola v r voller j b swenson c paola an analytical solution for a stefan problem with variable latent heat int j heat mass transfer 47 2004 5387 5390 and lorenzo trueba and voller j lorenzo trueba v r voller analytical and numerical solution of a generalized stefan problem exhibiting two moving boundaries with application to ocean delta formation j math anal appl 366 2010 538 549 a model associated with the formation of sedimentary ocean deltas is studied through a one phase stefan like problem with variable latent heat motivated by these works we consider a two phase stefan problem with variable latent of fusion and initial temperature and constant heat flux boundary conditions we obtain the sufficient condition on the data in order to have an explicit solution of a similarity type of the corresponding free boundary problem for a semi infinite material moreover the explicit solution given in the first quoted paper can be recovered for a particular case by taking a null heat flux condition at the infinity

stochastic evolution equations in umd banach spaces we discuss existence uniqueness and space time holder regular ity for solutions of the parabolic stochastic evolution equation du t au t f t u t dt b t u t dwh t t 2 0 t0 u 0 u0 where a generates an analytic c0 semigroup on a umd banach space e and wh is a cylindrical brownian motion with values in a hilbert space h we prove that if the mappings f 0 t e e and b 0 t e l h e satisfy suitable lipschitz conditions and u0 is f0 measurable and bounded then this problem has a unique mild solution which has trajectories in c 0 t d a provided 0 and 0 satisfy 1 2 vari ous extensions of this result are given and the results are applied to parabolic stochastic partial dierential equations

pseudodifferential operators on bochner spaces and an application we consider pseudodifferential operators with operator valued symbols a x acting on a umd banach space x assuming some regularity of holder type in x and mihlin type in we prove l p n x boundedness of such operators this result is then applied to the study of l p maximal regularity for nonautonomous parabolic evolution equations

a new approach to stochastic evolution equations with adapted drift abstract in this paper we develop a new approach to stochastic evolution equations with an unbounded drift a which is dependent on time and the underlying probability space in an adapted way it is well known that the semigroup approach to equations with random drift leads to adaptedness problems for the stochastic convolution term in this paper we give a new representation formula for the stochastic convolution which avoids integration of non adapted processes here we mainly consider the parabolic setting we establish connections with other solution concepts such as weak solutions the usual parabolic regularity properties are derived and we show that the new approach can be applied in the study of semilinear problems with random drift at the end of the paper the results are illustrated with two examples of stochastic heat equations with random drift

stochastic heat equation with random coefficients we prove the existence of a unique solution for a one dimensional stochastic parabolic partial differential equation with random and adapted coefficients perturbed by a two parameter white noise the proof is based on a maximal inequality for the skorohod integral deduced from ito s formula for this anticipating stochastic integral

approximation of the modified error function abstract in this article we obtain explicit approximations of the modified error function introduced in cho and sunderland 1974 as part of a stefan problem with a temperature dependent thermal conductivity this function depends on a parameter which is related to the thermal conductivity in the original phase change process we propose a method to obtain approximations which is based on the assumption that the modified error function admits a power series representation in accurate approximations are obtained through functions involving error and exponential functions only for the special case in which assumes small positive values we show that the modified error function presents some characteristic features of the classical error function such as monotony concavity and boundedness moreover we prove that the modified error function converges to the classical one when goes to zero

pathwise mild solutions for quasilinear stochastic partial differential equations abstract stochastic partial differential equations spdes have become a key modeling tool in applications yet there are many classes of spdes where the existence and regularity theory for solutions is not completely developed here we contribute to this aspect and prove the existence of mild solutions for a broad class of quasilinear cauchy problems including among others cross diffusion systems as a key application our solutions are local in time and are derived via a fixed point argument in suitable function spaces the key idea is to combine in a suitable way the classical theory of deterministic quasilinear parabolic partial differential equations pdes with recent theory of evolution semigroups we also show how to apply our theory to the shigesada kawasaki teramoto skt model furthermore we provide examples of blow up and ill posed operators which can occur after finite time showing that solutions can only be local in time for general quasilinear spdes while they might be global in time for special subclasses of problems

a method for the 2 d quasi isometric regular grid generation a method for the generation of quasi isometric boundary fitted curvilinear coordinate systems for arbitrary domains is developed on the basis of the theory of conformal quasi conformal and quasi isometric mappings and results from the non euclidean geometry concerning surfaces of constant curvature the method as it is proposed has an advantage over similar methods developed earlier in that the number of unknown parameters to be found is decreased strict boundaries for parameters are found and a simple and efficient process of identification of an unknown parameter is given the reliability of the method is assured by an existence and uniqueness theorem for quasi isometric maps between physical regions and geodesic quadrangles on surfaces of constant curvature which are used to constrict quasi isometric grids in physical domains we formulate the riemannian metric consistent with this theorem which is available analytically illustrations of this technique are given for various domains

initial boundary value problems and optimal control for nonautonomous parabolic systems a large class of linear nonautonomous parabolic systems in bounded domains is considered with control acting on the boundary through dirichlet or neumann conditions from the point of view of semigroup theory the results from rend sem mat univ padova 78 1987 pp 47 107 on fundamental solutions for abstract parabolic equations lecture notes in math vol 1223 springer verlag berlin heidelberg 1986 pp 1 11 on abstract homogeneous parabolic cauchy problems allow operators with varying domains and holder continuous coefficients to be handled a representation formula for solutions corresponding to square integrable control functions is derived and used to solve a linear quadratic regulator problem over finite time horizon by a direct study of the associated integral riccati equation

new exact solutions for an n 1 dimensional generalized boussinesq equation abstract the auxiliary differential equation approach and the symbolic computation system maple are employed to investigate an n 1 dimensional generalized boussinesq equation the exact solutions to the equation are constructed analytically under certain circumstances it is shown that many of the solutions obtained in this work are new solutions

nearly orthogonal two dimensional grid generation with aspect ratio control an improved method for nearly orthogonal grid generation is presented in this study the generating system is based on solution of a system of partial differential equations with finite difference discretization to prevent grid lines from collapsing onto each other the grid cell aspect ratio is controlled by functions that limit excessive ratios bounding all the aspect ratios is essential for high quality numerical approximations using such grid based methods as finite elements finite differences or finite volumes the influence of the number of grid points type of boundary and intensity of the grid quality control function and grid properties are investigated specification of both boundary point distribution on all sides and moving boundaries is used the proposed method is applied to various test problems from the literature this method is shown to provide a good balance between controlling grid orthogonality and cell aspect ratio c 2001 academic press

recursive numerical algorithm for conformal mapping in two dimensional hydrodynamics an original recursive numerical method rt algorithm for conformal mapping is presented based on the lavrentiev variational principle it is a powerful means for the solution of various two dimensional boundary value problems the rt algorithm can be used to solve internal and external hydrodynamics problems occurring in spacecraft research namely the calculation of fluid motions with local vorticity regions for external problems conformal mapping of the fluid flow area onto the outside of the unit circle is constructed for internal problems the area is mapped onto one of standard domains the unit circle or circular annulus fluid flows in a cylindrical tank with inner radial damping ribs and nearby an air brake with sharp edges with or without free eddies are discussed as examples

orthogonal grid generation in a 2d domain via the boundary integral technique a new numerical scheme is proposed for the generation of an orthogonal coordinate grid in an arbitrary simply connected two dimensional domain the scheme is robust and non iterative and is based on the conjunction of the familiar boundary integral technique with the covariant laplace equation method for mapping in the proposed scheme two types of problems are considered 1 boundary correspondence is specified on two adjacent sides of the boundary or 2 the distortion factor is specified in the product form f x h x q h

exact solutions of a class of nonlinear boundary value problems with moving boundaries presents a method for the construction of the exact solutions of nonlinear bvps in melting and evaporation processes the case of smooth functions of thermal conductivity is studied and illustrations of some specific nonlinearities given

stochastic integration in umd banach spaces in this paper we construct a theory of stochastic integration of processes with values in l h e where h is a separable hilbert space and e is a umd banach space i e a space in which martingale differences are unconditional the integrator is an h cylindrical brownian motion our approach is based on a two sided l p decoupling inequality for umd spaces due to garling which is combined with the theory of stochastic integration of l h e valued functions introduced recently by two of the authors we obtain various characterizations of the stochastic integral and prove versions of the ito isometry the burkholder davis gundy inequalities and the representation theorem for brownian martingales

lie symmetries and reductions of multi dimensional boundary value problems of the stefan type a new definition of lie invariance for nonlinear multi dimensional boundary value problems bvps is proposed by the generalization of known definitions to much wider classes of bvps the class of 1 3 dimensional nonlinear bvps of the stefan type modeling the process of melting and evaporation of metals is studied in detail using the definition proposed the group classification problem for this class of bvps is solved and some reductions with physical meaning to bvps of lower dimensionality are made examples of how to construct exact solutions of the 1 3 dimensional nonlinear bvp with the correctly specified coefficients are presented

stochastic evolution equations with random generators we prove the existence of a unique mild solution for a stochastic evolution equation on a hilbert space driven by a cylindrical wiener process the generator of the corresponding evolution system is supposed to be random and adapted to the filtration generated by the wiener process the proof is based on a maximal inequality for the skorohod integral deduced from the ito s formula for this anticipating stochastic integral

explicit solutions to the two phase stefan problem for storm type materials a reciprocal transformation is employed to reduce a two phase stefan problem in nonlinear heat conduction into a form which admits a class of exact solutions analogous to the classical neumann solution the problem is considered for materials of storm type rogers 1985 j phys a math gen 18 105 9 two related cases are considered one of them has a flux condition of the type q 0 t 1 2 q 0 0 and the existence and uniqueness of the solution is proved when q 0 satisfies a certain inequality which generalizes the work of tarzia 1981 q appl math 39 491 7 obtained for constant thermal coefficients the other one has a temperature condition on the fixed face and the existence and uniqueness is proved for all data

linear skorohod stochastic differential equations let andb be bounded processes on the wiener space p c 0 1 which are possibly anticipating the brownian motionw t t and let be a bounded random variable we deduce the existence and uniqueness of a solutionx for the linear equation with skorohod integral x t eta int limits 0 t sigma s x s dw s int limits 0 t b s x s ds t in 0 1 1 under rather weak assumptions on and no additional requirement onb and the description of the solutionx requires to study the family t t t 0 1 of transformationt t of into itself associated to 1 by the equation t t omega int limits 0 t wedge sigma s t s omega ds omega in omega t in 0 1

evolution equation of a stochastic semigroup with white noise drift we study the existence and uniqueness of the solution of a functionvalued stochastic evolution equation based on a stochastic semigroup whose kernel p s t y x is brownian in s and t the kernel p is supposed to be measurable with respect to the increments of an underlying wiener process in the interval s t the evolution equation is then anticipative and choosing the skorohod formulation we establish existence and uniqueness of a continuous solution with values in l r as an application we prove the existence of a mild solution of the stochastic parabolic equation dut xudt v dt x ru f t x u w dt x where v and w are brownian in time with respect to a common ltration in this case p is the formal backward heat kernel of x v dt x rx supported by the dgicyt grant no pb96 0087 ysupported by nsf international opportunities postdoctoral fellowship no int9600278 and nsf nato postdoctoral fellowship no dge 9633937 ams subject classi cation primary 60h15 secondary 60h07

application of a reciprocal transformation to a two phase stefan problem a reciprocal transformation is employed to reduce a two phase stefan problem in nonlinear heat conduction to a form which admits a class of exact solutions analogous to the classical newmann solution

two parametric solution to graded yang baxter equation and two parametric uuvgl 1 mod 1 algebra as a hopf algebra the authors discuss a two parametric solution of the graded yang baxter equation ybe and perform the yang baxterization to obtain the solution to the quantum ybe in the formalism developed previously they present the two parametric quantized superalgebra uuvgl 1 mod 1 and prove that this algebra is a hopf algebra with the hopf operations explicitly provided