uniform stabilization of wave equation with localized damping and acoustic boundary condition abstract in this paper we deal with stability of the nonlinear wave equation with acoustic boundary conditions to non locally reacting boundary

some nonlinear wave equations with acoustic boundary conditions abstract we prove the existence and uniqueness of global solutions to the mixed problem for the carrier equation u tt m u 2 dx u u t u t 0 with acoustic boundary conditions

growing scale free networks with tunable clustering we extend the standard scale free network model to include a triad formation step we analyze the geometric properties of networks generated by this algorithm both analytically and by numerical c

energy decay of a variable coefficient wave equation with memory type acoustic boundary conditions abstract we study the energy decay for a variable coefficient wave equation with memory type acoustic boundary conditions boundary memory is described by an integral term applying the riemannian geometry method we obtain the uniform energy decay under some conditions on the memory function and the coefficient matrix

on the nearest neighbor of the nearest neighbor in multidimensional continuous and quantized space the probability that an entity in a set of entities uniformly distributed in space is the nearest neighbor of its nearest neighbor is evaluated for generic distances in a multidimensional environment such an expression is then specialized for systems with norm based distances and for systems with quantized norm based distance examples for scalar products and sup norm are derived when applicable invariances with respect to the underlying distance and entities density are highlighted dimensionality effects are investigated

multiscale convergence and reiterated homogenisation this paper generalises the notion of two scale convergence to the case of multiple separated scales of periodic oscillations it allows us to introduce a multi scale convergence method for the reiterated homogenisation of partial differential equations with oscillating coefficients this new method is applied to a model problem with a finite or infinite number of microscopic scales namely the homogenisation of the heat equation in a composite material finally it is generalised to handle the homogenisation of the neumann problem in a perforated domain

multi scale young measures we introduce multi scale young measures to deal with problems where multi scale phenomena are relevant we prove some interesting representation results that allow the use of these families of measures in practice and illustrate its applicability by treating from this perspective multi scale convergence and homogenization of multiple integrals

on the wave equation with semilinear porous acoustic boundary conditions the goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary interior sources and a nonlinear boundary interior damping first applying the nonlinear semigroup theory we show the existence and uniqueness of local in time solutions the main difficulty in proving the local existence result is that the neumann boundary conditions experience loss of regularity due to boundary sources using an approximation method involving truncated sources and adapting the ideas in lasiecka and tataru 1993 28 we show that the existence of solutions can still be obtained second we prove that under some restrictions on the source terms then the local solution can be extended to be global in time in addition it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ode and depends on the behavior of the damping terms in several situations the obtained ode can be easily solved and the decay rates can be given explicitly third we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping then the solution ceases to exists and blows up in finite time moreover in either the absence of the interior source or the boundary source then we prove that the solution is unbounded and grows as an exponential function

existence and decay of solutions for a viscoelastic wave equation with acoustic boundary conditions abstract in this paper we consider a multi dimensional damped semilinear viscoelastic wave equation with variable coefficient and acoustic boundary conditions first we prove a local existence theorem by using the faedo galerkin approximations combined with a contraction mapping theorem second we show that under suitable conditions on the initial data and the relaxation function the solution exists globally in time and we prove the uniform decay rate of the energy

a linearized viscous compressible flow plate interaction with non dissipative coupling abstract we address semigroup well posedness for a linear compressible viscous fluid interacting at its boundary with an elastic plate we derive the model by linearizing the compressible navier stokes equations about an arbitrary flow state so the fluid pde includes an ambient flow profile u in contrast to model in 6 we track the effect of this term at the flow structure interface yielding a velocity matching condition involving the material derivative of the structure this destroys the dissipative nature of the coupling of the dynamics we adopt here a lumer phillips approach with a view of associating fluid structure solutions with a c 0 semigroup e a t t 0 on a chosen finite energy space of data given this approach the challenge becomes establishing the maximal dissipativity of an operator a yielding the flow structure dynamics

on a mixed problem with a nonlinear acoustic boundary condition for a non locally reacting boundaries abstract we discuss global solvability to the mixed problem for a nonlinear wave equation in domains with non locally reacting boundaries and nonlinear acoustic boundary condition we prove the existence and uniqueness of solution additionally using the method of nakao we demonstrate the decay of the associated energy stability

wave equation with porous nonlinear acoustic boundary conditions generates a well posed dynamical system we consider a structural acoustic wave equation with nonlinear acoustic boundary conditions this is a coupled system of second and first order in time partial differential equations with boundary conditions on the interface we prove wellposedness in the hadamard sense for strong and weak solutions the main tool used in the proof is the theory of nonlinear semigroups we present the system of partial differential equations as a suitable cauchy problem dw dt aw though the operator a is not maximally dissipative we are able to show that it is a translate of a maximally dissipative operator the obtained semigroup solution is shown to satisfy a suitable variational equality thus giving weak solutions to the system of pdes the results obtained i dispel the notion that the model does not generate semigroup solutions ii provide treatment of nonlinear models and iii provide existence of a correct state space which is invariant under the flow thus showing that physical model under consideration is a dynamical system the latter is obtained by eliminating compatibility conditions which have been assumed in previous work on the linear case

nearest neighbors by neighborhood counting finding nearest neighbors is a general idea that underlies many artificial intelligence tasks including machine learning data mining natural language understanding and information retrieval this idea is explicitly used in the k nearest neighbors algorithm knn a popular classification method in this paper this idea is adopted in the development of a general methodology neighborhood counting for devising similarity functions we turn our focus from neighbors to neighborhoods a region in the data space covering the data point in question to measure the similarity between two data points we consider all neighborhoods that cover both data points we propose to use the number of such neighborhoods as a measure of similarity neighborhood can be defined for different types of data in different ways here we consider one definition of neighborhood for multivariate data and derive a formula for such similarity called neighborhood counting measure or ncm ncm was tested experimentally in the framework of knn experiments show that ncm is generally comparable to vdm and its variants the state of the art distance functions for multivariate data and at the same time is consistently better for relatively large k values additionally ncm consistently outperforms heom a mixture of euclidean and hamming distances the standard and most widely used distance function for multivariate data ncm has a computational complexity in the same order as the standard euclidean distance function and ncm is task independent and works for numerical and categorical data in a conceptually uniform way the neighborhood counting methodology is proven sound for multivariate data experimentally we hope it works for other types of data

homogenization of linear and nonlinear transport equations we study the homogenization of the linear and nonlinear transport equations with oscillatory velocity fields two types of homogenized equations are derived for general n dimensional linear and nonlinear problems we derive homogenized equations by introducing additional independent variables to represent the small scales for the two dimensional linear transport equations we derive effective equations for the averaged quantities such equations take the form of either a degenerate non local diffusion equation with memory or a higher order hyperbolic equation to study the nonlinear transport equations we introduce the concept of two scale young measure and extend diperna s method to prove that it reduces to a family of dirac measures

uniform energy decay of a variable coefficient wave equation with nonlinear acoustic boundary conditions abstract a variable coefficient wave equation with nonlinear damped acoustic boundary conditions is considered the riemannian geometry method is applied to deal with the variable coefficients under some checkable conditions on the coefficients the uniform decay of the energy is achieved without any geometrical conditions on the shape of the dissipative portion of the boundary

well posedness and optimal decay rates for the wave equation with nonlinear boundary damping source interaction we establish subject to some natural additional assumptions imposed on the relation between the source and the damping both well posedness and effective optimal decay rates for the solutions of a semilinear model of the wave equation the theory presented allows to consider both superlinear and sublinear behaviours of the dissipation in the presence of unstructured sources

well posedness for a variable coefficient wave equation with nonlinear damped acoustic boundary conditions abstract we consider a variable coefficient wave equation with nonlinear damped acoustic boundary conditions well posedness in the hadamard sense for strong and weak solutions is proved by using the theory of nonlinear semigroups

polynomial decay of a variable coefficient wave equation with an acoustic undamped boundary condition abstract we consider a variable coefficient wave equation with an acoustic undamped condition this is a coupled system of second and first order in time partial differential equations with an acoustic boundary condition on the interface the riemannian geometry method is applied to deal with the variable coefficients under some checkable conditions on the coefficients we obtain the polynomial energy decay

strong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditions we consider a wave equation with semilinear porous acoustic boundary conditions this is a coupled system of second and first order in time partial differential equations with possibly semilinear boundary conditions on the interface the results obtained are i strong stability for the linear model ii exponential decay rates for the energy of the linear model and iii local exponential decay rates for the energy of the semilinear model this work builds on a previous result showing generation of a well posed dynamical system the main tools used in the proofs are i the stability theorem of arendt batty ii energy methods used in the study of a wave equation with boundary damping and iii an abstract result of i lasiecka applicable to hyperbolic like systems with nonlinearly perturbed boundary conditions

structure of a large social network we study a social network consisting of over 10 4 individuals with a degree distribution exhibiting two power scaling regimes separated by a critical degree k mathrm crit and a power law relation between degree and local clustering we introduce a growing random model based on a local interaction mechanism that reproduces the observed scaling features and their exponents we suggest that the double power law originates from two very different kinds of networks that are simultaneously present in the human social network

a general approach to lower semicontinuity and lower closure in optimal control theory a self contained approach to lower semicontinuity and lower closure evolves from an extension of relaxed control theory which is based on a central relative weak compactness criterion called tightness and relaxation in all but one variable two lower closure results for outer integral functionals with variable abstract time domain are developed the first of these has a convexity condition for the integrand and generalizes all similar results in the literature the second lower closure result is of a new kind among other things it implies a quite general version of fatou s lemma in several dimensions