global existence and nonexistence of solution for cauchy problem of two dimensional generalized boussinesq equations abstract in this paper we consider the cauchy problem of two dimensional generalized boussinesq type equation u t t u u t t 2 u f u 0 under the assumption that f u is a function with exponential growth at infinity and under some assumptions on the initial data we prove the existence and nonexistence of global weak solution there are very few works on boussinesq equation with nonlinear exponential growth term by potential well theory

global existence and exponential growth of solution for the logarithmic boussinesq type equation abstract in this paper we consider the boussinesq type equation associated with logarithmic nonlinear term and initial boundary value conditions by using potential well method combined with the logarithmic sobolev inequality we obtain the existence of global solution at last we show that the l 2 norm of the solution will grow up as an exponential function as time goes to infinity under some suitable conditions for initial data the result shows that the polynomial nonlinearity is a critical condition of blow up in finite time for the solutions of boussinesq equations

the regularized boussinesq equation instability of periodic traveling waves abstract in this work we study the linear instability of periodic traveling waves associated with a generalization of the regularized boussinesq equation by using analytic and asymptotic perturbation theory we establish sufficient conditions for the existence of exponentially growing solutions to the linearized problem and so the linear instability of periodic profiles is obtained with respect to applications of this approach we prove the linear nonlinear instability of cnoidal wave solutions for the modified regularized boussinesq equation and for a system of two coupled boussinesq equations

initial boundary value problem of the generalized cubic double dispersion equation in this paper the existence and the uniqueness of the global generalized solution and the global classical solution for the initial boundary value problem of the generalized cubic double dispersion equation are proved the nonexistence of global solution for the initial boundary value problem of the generalized cubic double dispersion equation is discussed

the cauchy problem for the generalized imbq equation in ws p rn in this paper the existence and the uniqueness of the global strong solution and the global classical solution for the cauchy problem of the multidimensional generalized imbq equation are proved the nonexistence of the global solution for the cauchy problem of the generalized imbq equation is discussed

congruences between derivatives of abelian l functions at s 0 let k k be a finite abelian extension of global fields we prove that a natural equivariant leading term conjecture implies a family of explicit congruence relations between the values at s 0 of derivatives of the dirichlet l functions associated to k k we also show that these congruences provide a universal approach to the refined abelian stark conjectures formulated by inter alia stark gross rubin popescu and tate we thereby obtain the first proofs of amongst other things the rubin stark conjecture and the refined class number formulas of both gross and tate for all extensions k k in which k is either an abelian extension of or is a function field

existence and blow up of solution of cauchy problem for the generalized damped multidimensional boussinesq equation we consider the existence both locally and globally in time and the blow up of solutions for the cauchy problem of the generalized damped multidimensional boussinesq equation

optimal narrow beam low sidelobe synthesis for arbitrary arrays the classical narrow main beam and low sidelobe synthesis problem is addressed and extended to arbitrary sidelobe envelopes in both one and two dimensional scenarios the proposed approach allows also to handle arbitrary arrays this extended basic synthesis problem is first rewritten as a convex optimization problem this problem is then transformed into either a linear program or a second order cone program that can be solved efficiently by readily available software the convex formulation is not strictly equivalent to the initial synthesis problem but arguments are given that establish that the obtained optimum is either identical or can be made as close as wanted to the desired one finally numerical applications and a comparison with a classical solution are presented to both confirm the optimality of the solution and illustrate the potentialities of the proposed approach

a simple algorithm to achieve desired patterns for arbitrary arrays a simple iterative algorithm which can be used to find array weights that produce array patterns with a given look direction and an arbitrary sidelobe specification is presented the method can be applied to nonuniform array geometries in which the individual elements have arbitrary and differing radiation patterns the method is iterative and uses sequential updating to ensure that peak sidelobe levels in the array meet the specification computation of each successive pattern is based on the solution of a linearly constrained least squares problem the constraints ensure that the magnitude of the sidelobes at the locations of the previous peaks takes on the prespecified values phase values for the sidelobes do not change during this process and problems associated with choosing a specific phase value are therefore avoided experimental evidence suggests that the procedure terminates in remarkably few iterations even for arrays with significant numbers of elements

pattern synthesis with multipoint accurate array response control in this paper the problem of pattern synthesis with antenna arrays is addressed and new approaches based on the recently developed accurate array response control textrm a 2 textrm rc algorithm are presented it is shown that the array weight vector obtained by the textrm a 2 textrm rc algorithm to control the normalized response at a single direction in each step belongs to a specific set thus an appropriate weight vector chosen from the intersection of weight vector sets corresponding to the desired responses at multiple directions is capable of simultaneously controlling those responses this results in the so called multipoint accurate array response control textrm ma 2 textrm rc algorithm moreover in order to avoid possible beam axis shift in pattern synthesis a modified textrm ma 2 textrm rc textrm m 2 textrm a 2 textrm rc algorithm is proposed by imposing a derivative constraint on the direction of beam axis representative numerical examples are provided to demonstrate the effectiveness of the proposed textrm ma 2 textrm rc and textrm m 2 textrm a 2 textrm rc algorithms for multipoint responses control and pattern synthesis

a flexible array synthesis method using quadratic programming a highly flexible synthesis method for an arbitrary array is proposed to best approximate a desired array pattern in a minimum mean square error sense the basic idea of the technique is to form a quadratic program with its cost function given by the mean square error between the array response and a properly selected pattern described by a known mathematical function this quadratic program can be a constrained or unconstrained optimization problem depending on the requirements of the desired array pattern in formulating the quadratic program no assumption has been made on the gain phase response or characteristics of the individual array elements therefore one can synthesize an array of arbitrary shape to any appropriate pattern with the characteristic of the array elements taken into consideration as long as one is able to model the array accurately the proposed method is used to synthesize arrays of different shapes linear as well as planar arrays including rectangular and circular planar arrays using a chebyshev polynomial or zero function as a design template to illustrate the feasibility of the proposed method

a note on the continuity of solutions of parametric linear programs this note shows that if a parametric linear program min cx ax b1 b2 x 0 has optimal solutions in an interval left underset raise0 3em hbox smash scriptscriptstyle theta bar theta right for then depending on degeneracy the solutions is a continuous vector function or a continuous point to set mapping in the latter case an algorithm is introduced to solve the problem and generate a continuous vector solution in left underset raise0 3em hbox smash scriptscriptstyle theta bar theta right

existence and scattering of small solutions to a boussinesq type equation of sixth order abstract in this paper we consider the existence and uniqueness of the global small solution as well as the small data scattering result to the cauchy problem for a boussinesq type equation of sixth order with the nonlinear term f u behaving as u p p 1 as u 0 in r n n 1 the main method and techniques used in our paper are the littlewood paley dyadic decomposition the stationary phase estimate and some properties of bessel function

congruences between derivatives of geometric l functions we prove a natural refinement of a theorem of lichtenbaum describing the leading terms of zeta functions of curves over finite fields in terms of weil etale cohomology we then use this result to prove the validity of chinburg s 3 conjecture for all abelian extensions of global function fields to prove natural refinements and generalisations of the refined stark conjectures formulated by amongst others gross tate rubin and popescu to prove a variety of explicit restrictions on the galois module structure of unit groups and divisor class groups and to describe explicitly the fitting ideals of certain weil etale cohomology groups in an appendix coauthored with k f lai and k s tan we also show that the main conjectures of geometric iwasawa theory can be proved without using either crystalline cohomology or drinfeld modules

a numerical pattern synthesis algorithm for arrays a numerical technique for pattern synthesis in arrays is presented for a given set of elements the technique allows one to find a set of array coefficients that steer the main beam in a given direction and yield sidelobes meeting a specified criterion if such a set of array coefficients exists if the pattern specifications cannot be met with the given elements the algorithm finds the best attainable pattern the advantage of this technique is that it can be used with an arbitrary set of array elements different elements in the array can have different element patterns and the array can have arbitrary nonuniform spacing between elements the synthesis technique is based on adaptive array theory the given array elements are assumed to be used as the elements of an adaptive array the main beam is pointed in the proper direction by choosing the steering vector for that direction and the sidelobes are controlled by introducing a large number of interfering signals at many angles throughout the sidelobe region the algorithm iterates on the interference powers until a suitable pattern is obtained

synthesis of minimax sidelobes for arbitrary arrays this paper presents a synthesis algorithm to minimize the maximum sidelobe level for an arbitrary array similar to dolph chebyshev patterns the minimax array patterns for arbitrary arrays have uniform sidelobes

generalized stark formulae over function fields we establish formulae of stark type for the stickelberger elements in the function field setting our result generalizes a work of hayes and a conjecture of gross it is used to deduce a p adic version of rubin stark conjecture and burns conjecture

remarks on modified improved boussinesq equations in one space dimension we study the existence and scattering of global small amplitude solutions to modified improved boussinesq equations in one dimension with nonlinear term graphic 1 behaving as a power graphic 2 as graphic 3 solutions are considered in graphic 4 space for all graphic 5 according to the value of s the power nonlinearity exponent p is determined liu liu 1996 indiana univ math j 45 797 816 obtained the minimum value of p greater than 8 at graphic 6 for sufficiently small cauchy data in this paper we prove that p can be reduced to be greater than graphic 7 at graphic 8 and the corresponding solution u has the time decay such as graphic 9 as graphic 10 we also prove non existence of non trivial asymptotically free solutions for graphic 11 under vanishing condition near zero frequency on asymptotic states 1 embed inline graphic 1 gif 2 embed inline graphic 2 gif 3 embed inline graphic 3 gif 4 embed inline graphic 4 gif 5 embed inline graphic 5 gif 6 embed inline graphic 6 gif 7 embed inline graphic 7 gif 8 embed inline graphic 8 gif 9 embed inline graphic 9 gif 10 embed inline graphic 10 gif 11 embed inline graphic 11 gif

global existence of solutions of cauchy problem for generalized system of nonlinear evolution equations arising from dna in this paper we prove that the cauchy problem for the generalized system of the nonlinear evolution equations arising from dna utt uxx uxxtt f v xx vtt vxxtt g v xx has a unique global generalized solutions in c2 0 hs hs a unique global classical solution and the sufficient conditions of blow up of solution in finite time are given we also prove that the cauchy problem has a unique global generalized solution in c2 0 wm p l wm p l and a unique global classical solution

asymptotic behavior and blow up of solutions to a nonlinear evolution equation of fourth order abstract in this paper the asymptotic behavior of the solution to the initial boundary value problem for a nonlinear evolution equation of fourth order 1 u t t a 1 u x x a 2 u x x t a 3 u x x t t u x x is studied the sufficient conditions for blow up of the solutions to the initial boundary value problems for eq 1 are given

small amplitude solutions of the generalized imbq equation in this paper the global existence of small amplitude solution for the cauchy problem of the multidimensional generalized imbq equation is proved moreover we obtain a nonlinear scattering result of the cauchy problem of the imbq equation for small initial data

cauchy problem for a damped generalized imbq equation in this paper we prove that the cauchy problem for the following damped generalized imbq equation utt uxx uxxtt 2uxxt f u xx x r t 0 admits a unique global generalized solution in c3 0 wm p r l r l2 r 1 p m 0 and a unique global classical solution in c3 0 wm p r l r l2 r m 2 1p moreover the blow up of the solution for the cauchy problem of damped generalized imbq equation is studied we also prove that the cauchy problem of the above mentioned equation has a unique global generalized solution in c2 0 hs r s 12 and a unique global classical solution in c2 0 hs r s 52 and discuss the blow up of the solution

global solution for a generalized boussinesq equation this paper considers the existence and uniqueness of the solution to the cauchy problem for a class of boussinesq equation proves the global existence and finite time blowup of the solution to the problem by the potential well method

global existence and blow up of wk p solutions for a class of nonlinear wave equations with dispersive term abstract in this paper we study the initial boundary value problem u tt u xxt u xxtt u x x 0 x t 0 u x 0 u 0 x u t x 0 u 1 x x u 0 t u 1 t 0 t 0 where 0 1 we first prove that if s c k r k 2 and satisfies h 1 s is bounded below i e s c 0 for some constant c 0 h 2 1 s c 1 0 s 1 d c 2 where 1 s s k 0 s 0 k 0 min c 0 0 u 0 x u 1 x w k p w 0 1 p 1 p then for any t 0 the problem admits a unique solution u x t w 2 0 t w k p w 0 1 p then the asymptotic behaviors and blow up of solutions are discussed in detail

pattern synthesis for arbitrary arrays using an adaptive array method this paper presents a new pattern synthesis algorithm for arbitrary arrays based on adaptive array theory with this algorithm the designer can efficiently control both mainlobe shaping and sidelobe levels the element weights optimize a weighted l sub 2 norm between desired and achieved patterns the values of the weighting function in the l sub 2 norm interpreted as imaginary jammers as in olen and compton s 1990 method are iterated to minimize exceedance of the desired sidelobe levels and minimize the absolute difference between desired and achieved mainlobe patterns the sidelobe control can be achieved by iteration only on sidelobe peaks in comparison to olen and compton s method the new algorithm provides a great improvement in mainlobe shaping control example simulations including both nonuniform linear and planar arrays are shown to illustrate the effectiveness of this algorithm