long time dynamics of kirchhoff wave models with strong nonlinear damping we study well posedness and long time dynamics of a class of quasilinear wave equations with a strong damping we accept the kirchhoff hypotheses and assume that the stiffness and damping coefficients are functions of the l2 norm of the gradient of the displacement we prove the existence and uniqueness of weak solutions and study their properties for a wide class of nonlinearities which covers the case of possible degeneration or even negativity of the stiffness coefficient and the case of a supercritical source term our main results deal with global attractors for strictly positive stiffness factors we prove that in the natural energy space endowed with a partially strong topology there exists a global finite dimensional attractor in the non supercritical case this attractor is strong in this case we also establish the existence of a fractal exponential attractor and give conditions that guarantee the existence of a finite number of determining functionals

global attractors for the wave equation with nonlinear damping based on a new a priori estimate method so called asymptotic a priori estimate the existence of a global attractor is proved for the wave equation utt kg ut u f u 0 on a bounded domain r3 with dirichlet boundary conditions the nonlinear damping term g is supposed to satisfy the growth condition c1 s c2 g s c3 1 s p where 1 p 0 is arbitrary the nonlinear term f is supposed to satisfy the growth condition f s c4 1 s q where q 2 it is remarkable that when 2 p 5 we positively answer an open problem in chueshov and lasiecka i chueshov i lasiecka long time behavior of second evolution equations with nonlinear damping math scuola norm sup 2004 and improve the corresponding results in feireisl e feireisl global attractors for damped wave equations with supercritical exponent j differential equations 116 1995 431 447

attractors for the degenerate kirchhoff wave model with strong damping existence and the fractal dimension abstract in this paper we study the long time behavior of the kirchhoff type wave equation in the space h 0 1 l 2 we prove the existence of the global attractor for the equation which covers the case of possible generation of the stiffness coefficient we also consider the geometrical property of the global attractor by means of the z 2 index we provide under suitable assumptions the fractal dimension of the global attractor is infinite

hyperbolic parabolic singular perturbation for quasilinear equations of kirchhoff type abstract we consider a hyperbolic parabolic singular perturbation problem for a quasilinear equation of kirchhoff type and obtain parameter dependent time decay estimates of the difference between the solutions of a quasilinear dissipative hyperbolic equation of kirchhoff type and the corresponding quasilinear parabolic equation for this purpose we show time decay estimates for hyperbolic parabolic singular perturbation problem for linear equations with a time dependent coefficient

sharp global nonlinear stability for temperature dependent viscosity convection with regard to the dependence of viscosity on temperature an unconditional non linear energy stability analysis for thermal convection according to navier stokes theory has not yet been developed we here analyse three models of fluid behaviour proposed by o a ladyzhenskaya we show that by using these theories we can develop an unconditional analysis directly two of the models lead directly to an unconditional development employing l2 theory while the third necessitates the introduction of a generalized energy also involving an l3 term the nonlinear stability boundaries in all three cases are sharp when compared with the instability thresholds of linear theory

global attractors for wave equations with nonlinear interior damping and critical exponents abstract in this paper we study the global attractors for wave equations with nonlinear interior damping we prove the existence regularity and finite dimensionality of the global attractors without assuming a large value for the damping parameter when the growth of the nonlinear terms is critical

finite dimensional exponential attractors for semilinear wave equations with damping abstract we consider the initial value problem for a class of second order evolution equations that includes among others the 3d sine gordon equation with damping and the 3d klein gordon type equations with damping we show the existence of a set with finite fractal dimension that contains the global attractor and attracts all smooth solutions at an exponential rate

global solvability for the kirchhoff equations in exterior domains of dimension three abstract we consider the initial boundary value problem for the kirchhoff equations in exterior domains or in the whole space of dimension three and show that these problems admit time global solutions provided the norms of the initial data in the usual sobolev spaces of appropriate order are sufficiently small we obtain uniform estimates of the l 1 r norms with respect to time variable at each point in the domain of solutions of initial boundary value problem for the linear wave equations we then show that the estimates above yield the unique global solvability for the kirchhoff equations

finite dimensional attractors for the kirchhoff equation with a strong dissipation abstract the paper studies the existence of the finite dimensional global attractors and exponential attractors for the dynamical system associated with the kirchhoff type equation with a strong dissipation u t t m u 2 u u t h u t g u f x it proves that the above mentioned dynamical system possesses a global attractor which has finite fractal dimension and an exponential attractor for application the fact shows that for the concerned viscoelastic flow the permanent regime global attractor can be observed when the excitation starts from any bounded set in phase space and the dimension of the attractor that is the number of degree of freedom of the turbulent phenomenon and thus the level of complexity concerning the flow is finite

source independent full waveform inversion of seismic data a set of seismic trace data is collected in an input data set that is first fourier transformed in its entirety into the frequency domain a normalized wavefield is obtained for each trace of the input data set in the frequency domain normalization is done with respect to the frequency response of a reference trace selected from the set of seismic trace data the normalized wavefield is source independent complex and dimensionless the normalized wavefield is shown to be uniquely defined as the normalized impulse response provided that a certain condition is met for the source this property allows construction of the inversion algorithm disclosed herein without any source or source coupling information the algorithm minimizes the error between data normalized wavefield and the model normalized wavefield the methodology is applicable to any 3 d seismic problem and damping may be easily included in the process

finite dimensionality and regularity of attractors for a 2 d semilinear wave equation with nonlinear dissipation we consider a semilinear wave equation defined on a two dimensional bounded domain with a nonlinear dissipation our main result is that the flow generated by the model is attracted by a finite dimensional global attractor in addition this attractor has additional regularity properties that depend on regularity properties of nonlinear functions in the equation to our knowledge this is a first result of this type in the context of higher dimensional wave equations

an attractor for the singularly perturbed kirchhoff equation with supercritical nonlinearity abstract we consider a quasilinear wave equation of kirchhoff type u t t 1 u 2 u u t f u g x where 0 is a small parameter without any growth restrictions on the nonlinearity f u we prove the existence of a finite dimensional global attractor on an appropriate bounded phase space the key step is the estimate of the difference between the solutions of a quasilinear dissipative hyperbolic equation of kirchhoff type and the corresponding quasilinear parabolic equation

a gronwall type lemma with parameter and its application to kirchhoff type nonlinear wave equation abstract the paper investigates a new gronwall type lemma with parameter 0 and establishes the uniform in time estimates as an application the paper studies the asymptotic behavior of the kirchhoff type equations with a strong dissipation and proves that the related solution semigroup possesses the global attractor

stability of attractors for the kirchhoff wave equation with strong damping and critical nonlinearities abstract the paper investigates longtime dynamics of the kirchhoff wave equation with strong damping and critical nonlinearities u t t 1 u 2 u u t h u t g u f x with 0 1 the well posedness and the existence of global and exponential attractors are established and the stability of the attractors on the perturbation parameter is proved for the ibvp of the equation provided that both nonlinearities h s and g s are of critical growth

existence and exponential decay for a kirchhoff carrier model with viscosity abstract in this work we study the existence of global solutions and exponential decay for the following nonlinear problem formula where m is a c 1 function m 0 0 0

an attractor for a nonlinear dissipative wave equation of kirchhoff type abstract in this paper we prove the existence and some absorbing properties of an attractor in a local sense for the initial boundary value problem of a quasilinear wave equation of kirchhoff type with a standard dissipation u t

optimal attractors of the kirchhoff wave model with structural nonlinear damping abstract the paper investigates the well posedness and longtime dynamics of the kirchhoff wave model with structural nonlinear damping u t t u 2 u u 2 u t f u g x with 1 2 1 we find a new critical exponent p n 2 n 2 p n 2 n 2 n 3 and show that when the growth exponent p of the nonlinearity f u is up to the range 1 p p i the ibvp of the equation is well posed and its solution is of additionally global regularity when t 0 ii for each 1 2 1 the related solution semigroup has in natural energy space h an optimal global attractor a whose compactness and attractiveness are in the regularized space h 1 where a lies and an optimal exponential attractor e whose compactness boundedness of the fractional dimension and the exponential attractiveness are in h 1 where e lies respectively iii the family of global attractors a 1 2 1 is upper semi continuous at each point 0 1 2 1 the paper breaks though the longstanding existed growth restriction 1 p p for p had been considered a uniqueness index deepens and extends the results in literature 6 25 27

on a class of nonlinear stochastic dynamical systems analysis of the transient behaviour abstract a class of nonlinear dynamical systems with random parameters and initial conditions is considered the transient time evolution of the mean value of the dependent variable is analyzed both by means of the stochastic averaging method and by adomian s decomposition method a proof of the equivalence of the decomposition method to the time series approximation of the dynamical response is provided an application is made to the van der pol equation and finally a comparison between the two previously discussed methods is given

global attractor for a model of extensible beam with nonlinear damping and source terms abstract this paper is concerned with the existence of a global attractor for the nonlinear beam equation with nonlinear damping and source terms u t t 2 u m u 2 d x u f u g u t h in r where is a bounded domain of r n m is a nonnegative real function and h l 2 the nonlinearities f u and g u t are essentially u u u u and u t r u t respectively with r 0 and this kind of problem models vibrations of extensible beams and plates

on the superlinear lazer mckenna conjecture abstract we prove the lazer mckenna conjecture for a superlinear elliptic problem of ambrosetti prodi type by constructing solutions with sharp peaks