chemotaxis with logistic source very weak global solutions and their boundedness properties abstract we consider the chemotaxis system u t u u v g u x t 0 0 v v u x t 0 in a smooth bounded domain r n where 0 and g generalizes the logistic function g u a u b u with 1 a 0 and b 0 a concept of very weak solutions is introduced and global existence of such solutions for any nonnegative initial data u 0 l 1 is proved under the assumption that 2 1 n moreover boundedness properties of the constructed solutions are studied inter alia it is shown that if b is sufficiently large and u 0 l has small norm in l for some n 2 then the solution is globally bounded finally in the case that additionally n 2 holds a bounded set in l can be found which eventually attracts very weak solutions emanating from arbitrary l 1 initial data the paper closes with numerical experiments that illustrate some of the theoretically established results

global existence and asymptotic behavior of classical solutions to a fractional logistic keller segel system abstract in this paper we consider a fractional parabolic elliptic keller segel system with a logistic source on r n first we establish the regularity of weak solutions of the fractional parabolic equation using blow up arguments combined with liouville type theorems next by the semigroup method and regularity results we prove the local existence and uniqueness of classical solutions moreover the global existence and boundedness of classical solutions for given initial data are obtained under some conditions finally we show the asymptotic behavior of the global solutions with strictly positive initial data

structural modification based on measured frequency response functions an exact eigenproperties reallocation a structural modification method based on frequency response functions is presented in terms of an inverse eigenvalue problem the design objective is to derive multiple lumped mass damper and stiffness modifications needed to reallocate eigenvalues and specify eigenvectors of an existing structure a frequency response function based substructure coupling concept is used to get the system dynamic equations a linear algebraic equation is finally obtained to identify the necessary structural modifications the exact structural modifications are determined the existence and uniqueness of exact solutions are also investigated the feasibility of structural modification is examined under the restrictions of structural modifications in the case where infinite many exact modifications can exist the proposed method was applied to an example structure based on experiment data the minimum stiffness modifications were calculated the result of application indicates that the suggested method can derive accurate structural changes just based on minimum number of measured frequency response functions

aggregation vs global diffusive behavior in the higher dimensional keller segel model abstract we consider the classical parabolic parabolic keller segel system u t u u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a smooth bounded domain r n it is proved that in space dimension n 3 for each q n 2 and p n one can find e 0 0 such that if the initial data u 0 v 0 satisfy u 0 l q e and v 0 l p e then the solution is global in time and bounded and asymptotically behaves like the solution of a discoupled system of linear parabolic equations in particular u v approaches the steady state m m as t where m is the total mass m u 0 of the population moreover we shall show that if is a ball then for arbitrary prescribed m 0 there exist unbounded solutions emanating from initial data u 0 v 0 having total mass u 0 m

domain structures in fourth order phase and ginzburg landau equations abstract in pattern forming systems competition between patterns with different wave numbers can lead to domain structures which consist of regions with differing wave numbers separated by domain walls for domain structures well above threshold we employ the appropriate phase equation and obtain detailed qualitative agreement with recent experiments close to threshold a fourth order ginzburg landau equation is used which describes a steady bifurcation in systems with two competing critical wave numbers the existence and stability regime of domain structures is found to be very intricate due to interactions with other modes in contrast to the phase equation the ginzburg landau equation allows a spatially oscillatory interaction of the domain walls thus close to threshold domain structures need not undergo the coarsening dynamics found in the phase equation far above threshold and can be stable even without phase conservation we study their regime of stability as a function of their quantized length domain structures are related to zig zags in two dimensional systems the latter are therefore expected to be stable only when quenched far enough beyond the zig zag instability

existence of solutions to chemotaxis dynamics with lipschitz diffusion and superlinear growth abstract this paper deals with the chemotaxis system with nonlinear diffusion and superlinear growth term f b b 1 b when n 3 it is shown that if 4 n 1 1 4 n n 2 3 then there exists a local solution to this system for any large data in the case of lipschitz growth marinoschi 2013 12 established the existence of local solutions to this system with sufficiently small initial data and showed that under a stronger assumption on the chemotactic sensitivity there exists a global solution with large initial data this paper develops the local solvability with lipschitz growth to the one with superlinear growth and allows the system to have a local solution with large initial data without any stronger assumption the key to including the superlinear growth lies in the yosida approximation of f in order to remove the smallness assumption on the initial data this paper provides a precise estimate for approximate solutions

a new result for global existence and boundedness of solutions to a parabolic parabolic keller segel system with logistic source abstract we consider the following fully parabolic keller segel system with logistic source ks u t u u v a u u 2 x t 0 v t v v u x t 0 over a bounded domain r n n 1 with smooth boundary the parameters a r 0 0 it is proved that if 0 then ks admits a global weak solution while if n 2 n c n 2 1 1 n 2 1 then ks possesses a global classical solution which is bounded where c n 2 1 1 n 2 1 is a positive constant which is corresponding to the maximal sobolev regularity apart from this we also show that if a 0 and n 2 n c n 2 1 1 n 2 1 then both u t and v t decay to zero with respect to the norm in l as t

a new result for boundedness in the quasilinear parabolic parabolic keller segel model with logistic source abstract the current paper considers the boundedness of solutions to the following quasilinear keller segel model with logistic source ks u t d u u u v u u 2 x t 0 v t v u v x t 0 d u u u v v 0 x t 0 u x 0 u 0 x v x 0 v 0 x x where r n n 1 is a bounded domain with smooth boundary 0 and 0 one novelty of this paper is that we find a new a priori estimate u max 1 0 max 1 0 e x t d x so that we develop new l p estimate techniques and thereby obtain the boundedness results where c g n and 0 0 are the constants which are corresponding to the gagliardo nirenberg inequality see lemma 2 2 and the maximal sobolev regularity see lemma 2 3 to our best knowledge this seems to be the first rigorous mathematical result which indicates the relationship between m and that yields the boundedness of the solutions where m is the exponent of diffusion term d u the above mentioned results have significantly improved and extended previous results of several authors

structural modifications in truncated systems by the rayleigh ritz method abstract this paper deals with the theoretical basis for the approximation of a modified structure eigensystem having only an incomplete set of modes and frequencies of the original model modal testing results and the amount of modification in the mass and stiffness matrices the method presented is based on the rayleigh ritz approximation and is optimal for the given information in the sense of minimizing a residual matrix norm the method is domenstrated for one specific case consisting of a bernoulli euler beam with a modified mid section

blow up in a higher dimensional chemotaxis system despite logistic growth restriction abstract we study radially symmetric solutions of a class of chemotaxis systems generalizing the prototype u t u u v u u x t 0 0 v m t u x t 0 in a ball r n with parameters 0 0 0 and 1 and m t 1 u x t d x it is shown that when n 5 and 3 2 1 2 n 2 then there exist initial data such that the smooth local in time solution of blows up in finite time this indicates that even superlinear growth restrictions may be insufficient to rule out a chemotactic collapse as is known to occur in the corresponding system without any proliferation

a parabolic elliptic elliptic attraction repulsion chemotaxis system with logistic source abstract this paper deals with the parabolic elliptic elliptic attraction repulsion chemotaxis system with logistic source u t d u u u v u w r u u 2 x t 0 0 v u v x t 0 0 w u w x t 0 under no flux boundary conditions in bounded domain with smooth boundary where r and are assumed to be positive when r 3 d u is assumed to satisfy d 0 0 d u c d u m 1 with m 1 and c d 0 it is proved that if 0 and 1 3 then for any given u 0 w 1 the system possesses a global and bounded classical solution for the case where d u 1 and n 3 the convergence rate of the solution is established when the random motion of the chemotactic species is neglected i e d u 0 and r n n 2 is a convex domain boundedness and the finite time blow up of the solution are investigated

how strong a logistic damping can prevent blow up for the minimal keller segel chemotaxis system in this paper we study the minimal keller segel model with a logistic source and obtain quantitative and qualitative descriptions of the competition between logistic damping and other ingredient especially chemotactic aggregation to guarantee boundedness and convergence more specifically we establish how precisely strong a logistic source can prevent blow up and then we obtain an explicit relationship between logistic damping and other ingredient especially chemotactic aggregation so that convergences are ensured and their respective convergence rates are explicitly calculated out known results in the literature are completed and refined furthermore our findings provide clues on how to produce blowup solutions for ks chemotaxis models with logistic sources

boundedness and finite time collapse in a chemotaxis system with volume filling effect abstract we consider the elliptic parabolic pde system u t u u u v x t 0 0 v m u x t 0 with nonnegative initial data u 0 having mean value m under homogeneous neumann boundary conditions in a smooth bounded domain r n the nonlinearities and are supposed to generalize the prototypes u u 1 p u u u 1 q 1 with p 0 and q r problems of this type arise as simplified models in the theoretical description of chemotaxis phenomena under the influence of the volume filling effect as introduced by painter and hillen k j painter t hillen volume filling and quorum sensing in models for chemosensitive movement can appl math q 10 2002 501 543 it is proved that if p q 2 n then all solutions are global in time and bounded whereas if p q 2 n q 0 and is a ball then there exist solutions that become unbounded in finite time the former result is consistent with the aggregation inhibiting effect of the volume filling mechanism the latter however is shown to imply that if the space dimension is at least three then chemotactic collapse may occur despite the presence of some nonlinearities that supposedly model a volume filling effect in the sense of painter and hillen

finite time blowup and global in time unbounded solutions to a parabolic parabolic quasilinear keller segel system in higher dimensions abstract in this paper we consider quasilinear keller segel type systems of two kinds in higher dimensions in the case of a nonlinear diffusion system we prove an optimal with respect to possible nonlinear diffusions generating explosion in finite time of solutions finite time blowup result in the case of a cross diffusion system we give results which are optimal provided one assumes some proper non decay of a nonlinear chemical sensitivity moreover we show that once we do not assume the above mentioned non decay our result cannot be as strong as in the case of nonlinear diffusion without nonlinear cross diffusion terms to this end we provide an example interesting by itself of global in time unbounded solutions to the nonlinear cross diffusion keller segel system with chemical sensitivity decaying fast enough in a range of parameters in which there is a finite time blowup result in a corresponding case without nonlinear cross diffusion

heteroclinic dynamics in a model of faraday waves in a square container we study periodic orbits associated with heteroclinic bifurcations in a model of the faraday system for containers with square cross section and single frequency forcing these periodic orbits correspond to quasiperiodic surface waves in the physical system the heteroclinic bifurcations are related to a continuum of heteroclinic connections in the integrable hamiltonian limit some of which persist in the presence of small damping the dynamics in the neighborhood of one of the heteroclinic bifurcations are examined in detail using approximate poincare maps with predictions that agree with numerical computations the results suggest a great richness of possible dynamics of faraday waves even in simple geometries and with single frequency forcing

boundedness in the higher dimensional chemotaxis haptotaxis model with nonlinear diffusion we consider the chemotaxis haptotaxis model ut d u u u v u w u 1 u w x t 0 vt v v u x t 0 wt vw x t 0 in a bounded smooth domain rn n 2 where and are positive parameters and the diffusivity d u is assumed to generalize the prototype d u u 1 with r under zero flux boundary conditions it is shown that for sufficiently smooth initial data u0 v0 w0 and 2n 1 the corresponding initial boundary problem possesses a unique global in time classical solution which is uniformly bounded this paper develops some lp estimate techniques and thereby extends boundedness results in n 3 to arbitrary space dimensions

blowup and global solutions in a chemotaxis growth system abstract we study a keller segel type of system which includes growth and death of the chemotactic species and an elliptic equation for the chemo attractant the problem is considered in bounded domains with smooth boundary as well as in the whole space in case the random motion of the chemotactic species is neglected a hyperbolic elliptic problem results for which we characterize blow up of solutions in finite time and existence of regular solutions globally in time in dependence on the systems parameters in this case convexity of the domain is needed for the parabolic elliptic problem in dimensions three and higher we establish global existence of regular solutions in a limiting case which is an extension of the results given by tello and winkler 2007

eigenvector error bounds and their applications to structural modification we have shown previously that some natural frequencies and mode shapes of a modified vibrating structure may be approximated from the incremental mass and stiffness matrices and from an incomplete set of measured natural frequencies and mode shapes for the unmodified system in addition error bounds were obtained for the natural frequencies of the modified structure we bound here the error in the approximated mode shapes portion nevertheless we have developed in ref 5 a method for approximating the modal parameters of a structure based on such data and have shown that the approximation is opti mal in a rayleigh ritz sense the associated inverse problem in which the incremental matrices are derived to meet prescribed modal data is posed and also partially solved in ref 6 naturally it is of impor tance to investigate the question how good are these approx imations clearly several error mechanisms contribute to the discrepancy between the modal parameters of the real structure and their analytical approximation first the real structure is a nonlinear continuous system whereas the model is linear and discrete second there are uncertainties regarding the physical properties and boundary conditions of the vibrat ing structure third the approximation is based on incom plete modal data for the unmodified structure e g only n natural frequencies and mode shapes are assumed to be known we have named this last effect the modal truncation error the analytical approximation is based mainly on data from experiments and we assume that the mechanisms of error resulting from nonlinearity discretization and uncer tainties in the physical parameters are negligible with respect to the dominant error caused by the modal truncation under such an assumption the possible errors of the natural frequen cies of the modified structure have been bounded using vari ous methods in a series of papers 7 10 the estimation of natural frequences and their range of variation is a main objective in the design and analysis of vibratory systems for some applications it is equally important to be able to predict mode shapes and error bounds for the modified structure this information is essential for the analysis of the dynamic stresses and strains bounding the nodal points and the ex treme values of the fundamental mode shapes is also of great

optimal support positions for a structure to maximize its fundamental natural frequency abstract a procedure and related theories are developed to find loci of optimal support positions for a structure to maximize its fundamental eigenvalue by increasing the support stiffness the concept of limit eigenvalue which is the upper bound of fundamental eigenvalue achieved by adding supports is introduced a condition is derived on which the fundamental eigenvalue can be reached to its limit eigenvalue a sensitivity formula of eigenvalues with respect to the change of support positions is also derived to set up an optimization problem and to obtain its optimal support positions it is found that the loci of m supports start from the maximum displacement position of the structure s first eigenfunction and end at certain positions on the nodal line of its m 1 th eigenfunction if the fundamental eigenvalue can reach its limit eigenvalue the suggested method is tested to find the loci for a beam and a plate structure

on explosions of solutions to a system of partial differential equations modelling chemotaxis a system of partial differential equations modelling chemotactic aggregation is analysed keller segel model conditions on the system of paramaters are given implying global existence of smooth solutions in two space dimensions and radially symmetric situations explosion of the bacteria concentration in finite time is shown for a class of initial values

boundedness in a quasilinear parabolic parabolic keller segel system with logistic source abstract we consider a quasilinear parabolic parabolic keller segel system involving a source term of logistic type 0 1 u t u u u v g u x t 0 t v t v v u x t 0 t with nonnegative initial data under neumann boundary condition in a smooth bounded domain r n n 1 here and are supposed to be smooth positive functions satisfying c 1 s p and c 1 s q s c 2 s q when s s 0 with some s 0 1 and we assume that g is smooth on 0 fulfilling g 0 0 and g s a s s 2 for all s 0 with constants a 0 and 0 within this framework it is proved that whenever q 1 for any sufficiently smooth initial data there exists a unique classical solution which is global in time and bounded our result is independent of p

structure optimization to enhance its natural frequencies based on measured frequency response functions abstract a measured frequency response function frf based structural modification method is presented to obtain optimal structural changes to enhance its natural frequencies structural dynamics modification sdm has been widely used for improvements of built in structures however the optimum design obtained by sdm differs from the true optimal solution when large modal changes happen in this paper a substructure coupling concept is used to get system equations in order to extend its use to large modal changes frf matrix of baseline structure and those of modification structures are coupled at the connection points under the condition of force equilibrium and geometric compatibility constraints thus exact modified modal properties can be calculated even for the case of large modal changes the optimal structural modification is calculated by combining eigenvalue sensitivities and eigenvalue reanalysis technique iteratively special attention is given to the case where baseline structure has some unidentified structural parameters to enlighten the advantage of this proposed method an application to the case of beam stiffener optimization indicates that the proposed method can provide an accurate optimal structural change just based on measured frfs without any kind of numerical models

limiting case of the sobolev inequality in bmo with application to the euler equations we shall prove a logarithmic sobolev inequality by means of the bmo norm in the critical exponents as an application we shall establish a blow up criterion of solutions to the euler equations

global existence of a two dimensional chemotaxis haptotaxis model with remodeling of non diffusible attractant abstract this paper deals with the cancer invasion model u t u u v u w u 1 u w x t 0 v t v v u x t 0 w t v w w 1 w u x t 0 in a bounded smooth domain r 2 with zero flux boundary conditions where and are positive parameters compared to previous mathematical studies the novelty here lies in first our treatment of the full parabolic chemotaxis haptotaxis system and second allowing for positive values of reflecting processes with self remodeling of the extracellular matrix under appropriate regularity assumptions on the initial data u 0 v 0 w 0 by using adapted l p estimate techniques we prove the global existence and uniqueness of classical solutions when is sufficiently large i e in the high cell proliferation rate regime

wrinkled tori and bursts due to resonant temporal forcing the effect of resonant temporal forcing on a system undergoing a hopf bifurcation with d4 square symmetry is studied the forcing breaks the continuous normal form symmetry of the governing amplitude equations but the d4 symmetry is preserved for this system it is shown that bursts with very large dynamic range may occur the bursts are associated with visits near solutions at infinity and are related to those found previously for the hopf bifurcation with broken d4 symmetry moehlis and knobloch physica d 135 2000 263 the regime in which an attracting quasiperiodic solution that exists in the absence of forcing wrinkles into chaos as the amplitude of the forcing increases is investigated in detail the overall behavior is governed by the approach of the resulting attractor to solutions at infinity windows with stable periodic solutions are found and associated with the traversal in parameter space through arnol d tongues other aspects of the dynamics are related to the presence of a new type of gluing bifurcation which we call a supergluing bifurcation 2001 elsevier science b v all rights reserved

global existence and asymptotic behavior of solutions to a two species chemotaxis system with two chemicals in this paper we investigate the competitive parabolic elliptic parabolic elliptic two species chemotaxis system with two chemicals in a smooth bounded domain rn n 1 the existence of global bounded classical solution is proved under mild assumptions on the initial data and appropriate conditions on the strength of the damping death effects moreover for the case when both competition parameters a1 and a2 lie in 0 1 it is shown that such solution stabilizes to spatially homogeneous equilibria in the large time limit

global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening abstract this paper deals with nonnegative solutions of the neumann initial boundary value problem for the parabolic chemotaxis system u t u u v u u 2 x t 0 v t v v u x t 0 in bounded convex domains r n n 1 with smooth boundary it is shown that if the ratio is sufficiently large then the unique nontrivial spatially homogeneous equilibrium given by u v 1 is globally asymptotically stable in the sense that for any choice of suitably regular nonnegative initial data u 0 v 0 such that u 0 0 the above problem possesses a uniquely determined global classical solution u v with u v t 0 u 0 v 0 which satisfies u t 1 l 0 and v t 1 l 0 as t

boundedness and global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with nonlinear logistic source abstract this paper deals with a fully parabolic chemotaxis system with nonlinear logistic source 0 1 u t u u v u 1 u r 1 v t v v u under homogeneous neumann boundary conditions in a smooth bounded convex domain r n with parameters 0 r 2 it is shown that if r 2 or r 2 and n 4 then for all sufficiently smooth initial data the associated initial boundary value problem 0 1 possesses a unique global in time classical solution that is bounded in 0 which satisfies lim sup t u t l max t 0 n 4 t 2 r t t r min r 1 2 moreover with the assumption u 0 0 and appropriate growth assumptions the globally asymptotical stability of 1 1 r 1 1 1 r 1 is established

a geometry constraint handling technique for stiffener layout optimization problem abstract beam stiffeners have frequently been used for raising natural frequencies of base structures in stiffener layout optimization problems most of the previous researches considering the position and or the length of the stiffener as design variables dealt with structures having just simple convex shapes such as a square or rectangle the reason was because concave shape structures have difficulties in formulating geometry constraints in this paper a new geometry constraint handling technique which can define both convex and concave feasible regions and measure a degree of geometry constraint violation was proposed evolution strategies ess was utilized as an optimization tool in addition the constraint handling technique of evoslinoc evolution strategies for scalar optimization with linear and nonlinear constraints was utilized to solve constrained optimization problems from numerical examples the proposed geometry constraint handling technique was verified and proved that the technique can easily be applied to structures in not only convex but also concave shapes even with a protrusion or interior holes

an optimal result for global existence and boundedness in a three dimensional keller segel stokes system with nonlinear diffusion abstract this paper investigates the following keller segel stokes system with nonlinear diffusion k s f n t u n n m n c x t 0 c t u c c c n x t 0 u t p u n x t 0 u 0 x t 0 under homogeneous boundary conditions of neumann type for n and c and of dirichlet type for u in a three dimensional bounded domains r 3 with smooth boundary where w 2 m 0 it is proved that if m 4 3 then for any sufficiently regular nonnegative initial data there exists at least one global boundedness solution for system k s f which in view of the known results for the fluid free system mentioned below see introduction is an optimal restriction on m

on a quasilinear parabolic elliptic chemotaxis system with logistic source abstract this paper deals with a quasilinear parabolic elliptic chemotaxis system with logistic source under homogeneous neumann boundary conditions in a smooth bounded domain for the case of positive diffusion function it is shown that the corresponding initial boundary value problem possesses a unique global classical solution which is uniformly bounded moreover if the diffusion function is zero at some point or a positive diffusion function and the logistic damping effect is rather mild we proved that the weak solutions are global existence finally it is asserted that the solutions approach constant equilibria in the large time for a specific case of the logistic source

heteroclinic dynamics in the nonlocal parametrically driven nonlinear schrodinger equation faraday waves are described under appropriate conditions by a damped nonlocal parametrically driven nonlinear schrodinger equation as the strength of the applied forcing increases this equation undergoes a sequence of transitions to chaotic dynamics the origin of these transitions is explained using a careful study of a two mode galerkin truncation and linked to the presence of heteroclinic connections between the trivial state and spatially periodic standing waves these connections are associated with cascades of gluing and symmetry switching bifurcations such bifurcations are located in the partial differential equations as well

sub logistic source can prevent blow up in the 2d minimal keller segel chemotaxis system it is well known that the neumann initial boundary value problem for the minimal keller segel chemotaxis system in a 2d bounded smooth domain has no blow ups for any presence of logistic source of cell kinetics here for a large class of cell kinetics including sub logistic sources we find an explicit condition involving the chemotactic strength the asymptotic damping rate and the initial mass of cells to ensure the uniform in time boundedness for the corresponding 2d neumann initial boundary value problem our finding in particular shows that sub logistic source can prevent blow up in 2d indicating that logistic damping is not the weakest damping to guarantee boundedness for the 2d keller segel minimal chemotaxis model

boundedness in a quasilinear parabolic parabolic keller segel system with subcritical sensitivity abstract we consider the quasilinear parabolic parabolic keller segel system u t d u u s u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a convex smooth bounded domain r n with n 1 it is proved that if s u d u c u with 2 n and some constant c 0 for all u 1 then the classical solutions to the above system are uniformly in time bounded provided that d u satisfies some technical conditions such as algebraic upper and lower growth resp decay estimates as u this boundedness result is optimal according to a recent result by the second author winkler 2010 27 which says that if s u d u c u for u 1 with c 0 and some 2 n n 2 then for each mass m 0 there exist blow up solutions with mass u 0 m in addition this paper also proves a general boundedness result for quasilinear non uniformly parabolic equations by modifying the iterative technique of moser alikakos alikakos 1979 1

resonant triad dynamics in weakly damped faraday waves with two frequency forcing abstract many of the interesting patterns seen in recent multi frequency faraday experiments can be understood on the basis of three wave interactions resonant triads in this paper we consider two frequency forcing and focus on a resonant triad occurring near the bicritical point where two pattern forming modes with distinct wavenumbers onset simultaneously this triad has been observed directly in the form of rhomboids and has also been implicated in the formation of quasipatterns and superlattices we show how the symmetries of the undamped unforced problem time translation time reversal and hamiltonian structure can be used when the damping is weak to obtain general scaling laws and additional qualitative properties of the normal form coefficients governing the pattern selection process near onset such features help to explain why this particular triad is seen only for certain low forcing ratios and predict the existence of drifting solutions and heteroclinic cycles we confirm the anticipated parameter dependence of the coefficients and investigate its dynamical consequences using coefficients derived numerically from a quasipotential formulation of the faraday problem due to zhang and vinals

a procedure for improving discrete substructure representation in dynamic synthesis n important problem in the dynamic analysis for flexible structures is that of determining the natural frequencies and associated natural modes of vibration particularly the lower ones complex structures are often represented by mathematical models such as finite element models possessing a very large number of degrees of freedom where the number can reach into the tens of thousands because of the large number of degrees of freedom a direct iterative method for obtaining a partial eigensolution know as subspace iteration was developed the subspace iteration method has a long history an extensive bibliography is given in ref 1 and the current status of the method is discussed in refs 2 4 in the context of structural dynamics even the subspace iteration method however can be overwhelmed by the large number of degrees of freedom in the mathematical model so that a method for prior reduction of the number of degrees of freedom is desirable complex structures are often modeled by breaking the structure into a number of simpler components or substructures the substructure models are then coupled together to form the whole structure model the technique is known as substructure synthesis and its origin can be found in refs 5 and 6 the idea of refs 5 and 6 is to represent the motion of each substructure by a set of substructure normal modes obtained by solving an eigenvalue problem for each substructure then each substructure is represented in the synthesis process by a reduced number of lower substructure modes the synthesis leads to an eigenvalue problem for the assembled structure of a substantially smaller order than that of the original formulation the price paid in reducing the order of the eigenvalue problem is that its solution is only an approximation of the actual eigensolution of the original structure

boundedness vs blow up in a chemotaxis system abstract we determine the critical blow up exponent for a keller segel type chemotaxis model where the chemotactic sensitivity equals some nonlinear function of the particle density assuming some growth conditions for the chemotactic sensitivity function we establish an a priori estimate for the solution of the problem considered and conclude the global existence and boundedness of the solution furthermore we prove the existence of solutions that become unbounded in finite or infinite time in that situation where this a priori estimate fails

large time behavior of solution to a fully parabolic chemotaxis haptotaxis model in higher dimensions abstract this paper deals with the chemotaxis haptotaxis model of cancer invasion u t u u v u w u 1 u w x t 0 v t v v u x t 0 w t v w x t 0 in a bounded smooth domain r n with zero flux boundary conditions where and are positive parameters it is shown that if is suitably large then for all sufficiently smooth initial data the associated initial boundary value problem possesses a unique global in time classical solution that is bounded in 0 and if the initial data w 0 is small w becomes asymptotically negligible moreover we prove that when domain is convex 1 1 0 is globally asymptotically stable provided that u 0 0 and thereby extends the result of hillen et al 2013 18 to the higher space dimensions

a new result for global solvability and boundedness in the n dimensional quasilinear chemotaxis model with logistic source and consumption of chemoattractant abstract we consider the following chemotaxis model u t d u u u v u u 2 x t 0 v t v u v x t 0 d u u u v v 0 x t 0 u x 0 u 0 x v x 0 v 0 x x on a bounded domain r n n 1 with smooth boundary and are positive constants here d is supposed to be smooth positive function satisfying d u c d u 1 m 1 for all u 0 with some c d m 0 besides appropriate smoothness assumptions in this paper it is only required that m 1 2 1 max 1 s 2 0 s v 0 l 2 3 if n 2 1 if n 3 then for any sufficiently smooth initial data there exists a classical solution which is global in time and bounded where 0 is a positive constant which is corresponding to the maximal sobolev regularity the results of this paper extends the results of jin j differential equations 263 9 2017 5759 5772 who proved the possibility of boundness of weak solutions in the case m 1 and n 3 to the best of our knowledge this is the first result which gives the relationship between m and that yields to the boundedness of the solution

upper and lower bounds for the natural frequencies of modified structures based on truncated modal testing results abstract a frequently encountered engineering problem is the prediction of the natural frequencies of a modified structure based on a truncated set of modes and frequencies of the unmodified structure modal testing results and on the known modification matrices in this paper upper and lower bounds for such an approach are derived

temporal forcing of small amplitude waves in anisotropic systems we investigate the effect of resonant temporal forcing on an anisotropic system that exhibits a hopf bifurcation to obliquely traveling waves in the absence of this forcing we find that the forcing can excite various phase locked standing wave structures rolls rectangles and cross rolls at onset at most one of the two char22 rolls or rectangles char22 is stable the cross rolls can arise in a secondary bifurcation and can be stable experimentally they would appear as a periodic switching between a structure in which the zig component dominates and one with a dominating zag structure since there are two symmetry related states of this kind one may expect disordered structures to arise due to the breakup of the pattern into domains the results are consistent with recent experiments on electroconvection in nematic liquid crystals by de la torre ju arez and rehberg phys rev a 42 2096 1990 we also apply the general analysis to a model of the behavior near a lifshitz point where the angle of obliqueness vanishes this analysis indicates that phase locked standing rectangles are always unstable in this parameter regime

on blow up criteria of smooth solutions to the 3 d euler equations in a bounded domain abstract we show that a smooth solution of the 3 d euler equations in a bounded domain breaks down if and only if a certain norm of vorticity blows up at the same time here this norm is weaker than bmo norm

global existence and asymptotic behavior of classical solutions to a parabolic elliptic chemotaxis system with logistic source on rn in the current paper we consider the following parabolic elliptic semilinear keller segel model on rnrn ut u u v au bu2 x rn t 0 0 i v u x rn t 0 where 0 a 0 b 0 are constant real numbers and n is a positive integer we first prove the local existence and uniqueness of classical solutions u x t u0 v x t u0 u x t u0 v x t u0 with u x 0 u0 u0 x u x 0 u0 u0 x for various initial functions u0 x u0 x next under some conditions on the constants a b a b and the dimension n we prove the global existence and boundedness of classical solutions u x t u0 v x t u0 u x t u0 v x t u0 for given initial functions u0 x u0 x finally we investigate the asymptotic behavior of the global solutions with strictly positive initial functions or nonnegative compactly supported initial functions under some conditions on the constants a b a b and the dimension n we show that for every strictly positive initial function u0 u0 limt supx rn u x t u0 ab v x t u0 ab 0 and that for every nonnegative initial function u0 u0 with non empty and compact support supp u0 supp u0 there are 0 clow u0 cup u0 such that limt sup x ct u x t u0 ab v x t u0 ab 0 0 c clow u0 and limt sup x ct u x t u0 v x t u0 0 c cup u0

boundedness in the higher dimensional quasilinear chemotaxis growth system with indirect attractant production abstract this paper deals with the following quasilinear chemotaxis growth system u t d u u u v u 1 u x t 0 v t v v w x t 0 w t w u x t 0 in a smoothly bounded domain r n n 3 under zero flux boundary conditions the parameters and are positive and the diffusion function d u is supposed to generalize the prototype d u d 0 u with d 0 0 and r under the assumption 1 4 n it is proved that whenever 0 0 and 0 for any given nonnegative and suitably smooth initial data u 0 v 0 w 0 satisfying u 0 0 the corresponding initial boundary problem possesses a unique global solution which is uniformly in time bounded the novelty of the paper is that we use the boundedness of the v t w 1 s with s 1 2 n n 2 to estimate the boundedness of v t l 2 q q 1 moreover the result in this paper can be regarded as an extension of a previous consequence on global existence of solutions by hu et al 2016 under the condition that d u 1 and n 3

boundedness of solutions to a quasilinear parabolic elliptic keller segel system with logistic source abstract we study global solutions of a class of chemotaxis systems generalizing the prototype u t u 1 m 1 u u u 1 q 1 v a u b u r x t 0 0 v v u x t 0 in a bounded domain r n n 1 with smooth boundary with parameters m 1 r 1 a 0 b q 0 it is shown that when q 1 max r m 2 n or b b 0 n r m 2 r m n 2 r 2 if q 1 r then for any sufficiently smooth initial data there exists a classical solution which is global in time and bounded the results improve the results of wang et al 2014 37 and cao and zheng 2014 6

direct component modal synthesis technique for system dynamic analysis a method for substructure modal synthesis to determine the modal parameters of a structure is investigated the order of the solution matrix does not depend on the number of substructure modes used instead it depends only on the number of connections between substructures the eigensolution determined by this method is exact since the system dynamic matrix equation is not needed in this method numerical computations required for the solution are drastically reduced the eigensolutions of the system in any frequency range can be obtained independently computation is reduced because lower or higher eigensolutions outside the interested frequency range are not required to be calculated the results obtained by this technique and the analytical method are compared and they are identical

boundedness in quasilinear keller segel systems of parabolic parabolic type on non convex bounded domains abstract this paper deals with the quasilinear fully parabolic keller segel system u t d u u s u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a bounded domain r n with smooth boundary n n the diffusivity d u is assumed to satisfy some further technical conditions such as algebraic growth and d 0 0 which says that the diffusion is allowed to be not only non degenerate but also degenerate the global in time existence and uniform in time boundedness of solutions are established under the subcritical condition that s u d u k u e for u 0 with 2 n k 0 and e 0 when d 0 0 this paper represents an improvement of tao and winkler 17 because the domain does not necessarily need to be convex in this paper in the case r n and d 0 0 uniform in time boundedness is an open problem left in a previous paper 7 this paper also gives an answer to it in bounded domains

energy type estimates and global solvability in a two dimensional chemotaxis haptotaxis model with remodeling of non diffusible attractant this paper deals with the coupled chemotaxis haptotaxis model ut u u v u w u 1 u w x t 0 0 v u v x t 0 wt vw w 1 w u x t 0 which was initially proposed by chaplain and lolas 2006 10 to describe the interactions between cancer cells the matrix degrading enzyme and the host tissue in a process of cancer cell invasion of tissue extracellular matrix here r2 is a bounded domain with smooth boundary and and are positive parameters as compared to previous mathematical studies the novelty here consists of allowing for positive values of reflecting processes of self remodeling of the extracellular matrix under zero flux boundary conditions it is shown that for any sufficiently smooth initial data u0 w0 satisfying first order compatibility conditions the model admits a unique global smooth solution a crucial ingredient in the proof is an energy like inequality which given t 0 yields boundedness of u t in llogl this serves as a starting point for a bootstrap argument used to derive higher regularity estimates sufficient for global extensibility of solutions

boundedness of solutions to a quasilinear parabolic parabolic keller segel system with a logistic source abstract we study global solutions of a class of chemotaxis systems generalizing the prototype u t u u u v a u b u r x t 0 v t v v u x t 0 in a bounded domain r n n 1 with smooth boundary u u 1 u u u 1 1 and the parameters r 1 a 0 b 0 and r it is proved that if 0 max r 1 2 n or b is big enough if r 1 then the classical solutions to the above system are uniformly in time bounded our results improve the results of wang et al 2014 28 and cao 2014 3 and also enlarge the range of the results of tao and winkler 2012 25 and ishida et al 2014 14