a new phenomenon in the critical exponent for structurally damped semi linear evolution equations abstract in this paper we find the critical exponent for global small data solutions to the cauchy problem in r n for dissipative evolution equations with power nonlinearities u p or u t p u t t u t u u p u t p here n 0 with 2 we show that the critical exponent for each of the two nonlinearities is related to each of the two possible asymptotic profiles of the linear part of the equation which are described by the diffusion equations v t v 0 w t w 0 the nonexistence of global solutions in the critical and subcritical cases is proved by using the test function method under suitable sign assumptions on the initial data and lifespan estimates are obtained by assuming small initial data in sobolev spaces we prove the existence of global solutions in the supercritical case up to some maximum space dimension n and we derive l q estimates for the solution for q 1 for 2 the result holds in any space dimension n 1 the existence result also remains valid if and or are fractional

local solvability and loss of smoothness of the navier stokes maxwell equations with large initial data abstract the existence of a local in time unique solution and loss of smoothness of a full magneto hydro dynamics mhd system are considered for periodic initial data the result is proven using fujita kato s method in l 1 based for the fourier coefficients functional spaces enabling us to easily estimate nonlinear terms in the system as well as solutions to maxwell s equations a loss of smoothness result is shown for the velocity and magnetic field it comes from the damped wave operator which does not have any smoothing effect

scaling variables and asymptotic expansions in damped wave equations abstract we study the long time behavior of small solutions to the nonlinear damped wave equationeu u a u n u u u r 0 whereeis a positive not necessarily small parameter we assume that the diffusion coefficienta converges to positive limitsa as and that the nonlinearity n u u u vanishes sufficiently fast asu 0 introducing scaling variables and using various energy estimates we compute an asymptotic expansion of the solutionu in powers of 1 2as and we show that this expansion is entirely determined up to the second order by a linear parabolic equation which depends only on the limiting valuesa in particular this implies that the small solutions of the damped wave equation behave for large like those of the parabolic equation obtained by settinge 0

convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping we consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time asymptotically the hyperbolic model may be viewed as isentropic euler equations with friction term added to the momentum equation to model gas flow through a porous media in this case our result justifies darcy s law time asymptotically our model may also be viewed as an elastic model with damping

global existence of solutions for a weakly coupled system of semilinear damped wave equations abstract in this paper we consider the cauchy problem for a weakly coupled system of semilinear damped wave equations we prove the global existence of solutions for small data in the supercritical case for any space dimension we also give estimates of the weighted energy of solutions and in a special case we prove an almost optimal estimate moreover in the subcritical case we give an almost optimal estimate of the lifespan from both above and below

asymptotic behavior of solutions for the damped wave equation with slowly decaying data abstract we consider the cauchy problem for the damped wave equation u t t u u t u 1 u t x r r n and the heat equation t 1 t x r r n if the data is small and slowly decays likely c 1 1 x k n 0 k 1 then the critical exponent is c k 1 2 k n for the semilinear heat equation in this paper it is shown that in the supercritical case there exists a unique time global solution to the cauchy problem for the semilinear heat equation in any dimensional space r n whose asymptotic profile is given by 0 t x r n e x y 2 4 t 4 t n 2 c 1 1 y 2 k n 2 d y provided that the data 0 satisfies lim x x k n 0 x c 1 0 even in the semilinear damped wave equation in the supercritical case a time global solution u with the data u u t 0 x u 0 u 1 x is shown in low dimensional spaces r n n 1 2 3 to have the same asymptotic profile 0 t x provided that lim x x k n u 0 u 1 x c 1 0 those proofs are given by elementary estimates on the explicit formulas of solutions

lp decay problem for the dissipative wave equation in odd dimensions abstract consider the cauchy problem in odd dimensions for the dissipative wave equation t u 0 in r 2 n 1 0 with u t u t 0 u 0 u 1 because the l 2 estimates and the l estimates of the solution u t are well known in this paper we pay attention to the l p estimates with 1 p 2 in particular p 1 of the solution u t for t 0 in order to derive l p estimates we first give the representation formulas of the solution u t t s t u 0 s t u 0 u 1 and then we directly estimate the exact solution s t g and its derivative t s t g of the dissipative wave equation with the initial data u 0 u 1 0 g in particular when p 1 and n 1 we get the l 1 estimate u t l 1 c e t 4 u 0 w n 1 u 1 w n 1 1 c u 0 l 1 u 1 l 1 for t 0

integrable lattice models for conjugate a 1 n a new class of a 1 n integrable lattice models is presented these are interaction round a face models based on fundamental nimrep graphs associated with the a 1 n conjugate modular invariants there being a model for each value of the rank and level the boltzmann weights are parametrized by elliptic theta functions and satisfy the yang baxter equation for any fixed value of the elliptic nome q at q 0 the models provide representations of the hecke algebra and are expected to lead in the continuum limit to coset conformal field theories related to the a 1 n conjugate modular invariants

existence and non existence of global solutions of the cauchy problem for higher order semilinear pseudo hyperbolic equations abstract we consider the cauchy problem for a higher order pseudo hyperbolic equation using the l p l q type estimation for the corresponding linear problem the existence and non existence criteria of global solutions are found the existence and uniqueness of smooth global solutions are also investigated we also establish the behavior of solutions and their derivatives as t

global existence of small data solutions for wave models with super exponential propagation speed abstract we consider semi linear classical damped wave models with time dependent speed of propagation and time dependent dissipation the right hand side is a power nonlinearity which can be interpreted only as a source term we are interested in the interplay of time dependent coefficients on the global existence of small data solutions the considerations are divided into two cases depending on the behavior of the propagation speed the super exponential and the sub exponential case in this paper we study the super exponential case one main tool of our approach is the use of matsumura type estimates for a family of cauchy problems depending on a parameter

wave equations with time dependent dissipation ii effective dissipation abstract this article is intended to present a construction of structural representations of solutions to the cauchy problem for wave equations with time dependent dissipation above scaling these representations are used to give estimates of the solution and its derivatives based on l q r n q 2 the article represents the second part within a series in jens wirth wave equations with time dependent dissipation i non effective dissipation j differential equations 222 2 2006 487 514 weak dissipations below scaling were discussed

optimal decay rate of solutions for cahn hilliard equation with inertial term in multi dimensions abstract the cauchy problem of the cahn hilliard equation with inertial term is considered based on green s function method together with energy estimates we get the global in time existence and optimal decay rate of solutions furthermore the viscous case is investigated in the last section

blackish fractal balls the blackish area mu of crumpled paper balls of dimension d 2 5 obtained through the immersion of such objects in a black solution or with the aid of a ballistic painting technique is investigated among other scaling relations the authors find that in the first case mu approximately l1 39 or 0 16 and in the second case mu approximately l1 24 or 0 12 where l is the unfolded size

old and new link polynomials from the theory of exactly solvable models abstract a general theory is presented to construct link polynomials topological invariants for knots and links from exactly solvable integrable models representations of the braid group and the markov traces on the representations are made through the general theory which is based on fundamental properties of the models various examples leading to alexander jones kauffman and new link polynomials are explicitly shown in a word the soliton theory contains an essence of the knot theory

critical exponent for the cauchy problem to the weakly coupled damped wave system abstract in this paper we consider a system of weakly coupled semilinear damped wave equations we determine the critical exponent for any space dimensions our proof of the global existence of solutions for supercritical nonlinearities is based on a weighted energy method whose multiplier is appropriately modified in the case where one of the exponent of the nonlinear term is less than the so called fujita s critical exponent we also give estimates of the lifespan of solutions from above for subcritical nonlinearities

weighted l2 estimates for dissipative wave equations with variable coefficients abstract we establish weighted l 2 estimates for the wave equation with variable damping u t t u a u t 0 in r n where a x a 0 1 x with a 0 0 and 0 1 in particular we show that the energy of solutions decays at a polynomial rate t n 2 1 if a x a 0 x for large x we derive these results by strengthening significantly the multiplier method this approach can be adapted to other hyperbolic equations with damping

decay of solutions for a semilinear system of elastic waves in an exterior domain with damping near infinity abstract we show that the solutions of a semilinear system of elastic waves in an exterior domain with a localized damping near infinity decay in an algebraic rate to zero we impose an additional condition on the lame coefficients it seems that this restriction cannot be overcome by using the two finite speed propagation of the elastic model since we do not assume compact support on the initial data and because the dissipation does not have compact support the decay rates obtained for the total energy of the linear problem and the l 2 norm of the solution improve previous results for the semilinear problem the decay rates in this paper seem to be the first contribution mainly in the context of initial data without compact support and localized dissipation

damped wave equation in the subcritical case abstract we study large time asymptotics of small solutions to the cauchy problem for the one dimensional nonlinear damped wave equation 1 v tt v t v xx v 1 0 x r t 0 v 0 x v 0 x v t 0 x v 1 x in the sub critical case 2 3 2 we assume that the initial data v 0 1 x 1 v 1 l l 1 a a 0 1 where l 1 a l 1 l 1 a a l 1 x 1 x 2 also we suppose that the mean value of initial data r v 0 x v 1 x dx 0 then there exists a positive value such that the cauchy problem 1 has a unique global solution v t x c 0 l l 1 a satisfying the following time decay estimate v t l c t 1 for large t 0 here 2 3 2

operator content of the cyclic solid on solid models the operator content of the cyclic solid on solid models is derived under general boundary conditions by mapping the row to row transfer matrix onto the six vertex model and xxz heisenberg chain for the shift boundary conditions the dimensions and spins of the primary operators are derived analytically from finite size corrections to the scaling spectra the full operator content agrees with results for a quantum chain model having the same local symmetry

global asymptotics of solutions to the cauchy problem for the damped wave equation with absorption abstract we consider the cauchy problem for the damped wave equation with absorption u t t u u t u 1 u 0 t x r r n the behavior of u as t is expected to be same as that for the corresponding heat equation t 1 0 t x r r n in the subcritical case 1 c n 1 2 n there exists a similarity solution w b t x with the form t 1 1 f x t depending on b lim x x 2 1 f x 0 our first aim is to show the decay rates u t l 2 u t l 1 u t l 2 o t 1 1 n 4 t 1 1 n 2 1 t 1 1 1 2 n 4 provided that the initial data without initial data size restriction spatially decays with reasonable polynomial order the decay rates are sharp in the sense that they are same as those of the similarity solution the second aim is to show that the gauss kernel is the asymptotic profile in the supercritical case which has been shown in case of one dimensional space by hayashi kaikina and naumkin n hayashi e i kaikina p i naumkin asymptotics for nonlinear damped wave equations with large initial data preprint 2004 we show this assertion in two and three dimensional space to prove our results both the weighted l 2 energy method and the explicit formula of solutions will be employed the weight is an improved one originally developed in y todorova b yordanov critical exponent for a nonlinear wave equation with damping j differential equations 174 2001 464 489

the lp lq estimates of solutions to one dimensional damped wave equations and their application to the compressible flow through porous media we first obtain the lp lq estimates of solutions to the cauchy problem for one dimensional damped wave equation vtt vxx vt 0 v vt t 0 v0 v1 x x t r r corresponding to that for the parabolic equation t xx 0 t 0 v0 v1 x the estimates are shown by v t e t 2v0 t v0 t 2lp ct 121q 1p 1 v0 v1 lq t 1 etc for 1 q p to show the explicit formula of the damped wave equation will be used to apply the estimates to nonlinear problems is the second aim we will treat the system of a compressible flow through porous media the solution is expected to behave as the diffusion wave which is the solution to the porous media equation due to the darcy law when the initial data has the same constant state at a sharp lp convergence rate for p 2 has been recently obtained by nishihara proc roy soc edinburgh sect a 133a 2003 1 20 by choosing a suitably located diffusion wave we will show the l1 convergence applying

topological crossovers in the forced folding of self avoiding matter abstract we study the scaling properties of forced folding of thin materials of different geometry the scaling relations implying the topological crossovers from the folding of three dimensional plates to the folding of two dimensional sheets and further to the packing of one dimensional strings are derived for elastic and plastic manifolds these topological crossovers in the folding of plastic manifolds were observed in experiments with predominantly plastic aluminum strips of different geometry elasto plastic materials such as paper sheets during the fast folding under increasing confinement force are expected to obey the scaling force diameter relation derived for elastic manifolds however in experiments with paper strips of different geometry we observed the crossover from packing of one dimensional strings to folding two dimensional sheets only because the fractal dimension of the set of folded elasto plastic sheets is the thickness dependent due to the strain relaxation after a confinement force is withdrawn

symmetries of the octonionic root system of e8 octonionic root system of e8 is decomposed as the 9 sets of hurwitz integers each set satisfying the binary tetrahedral group structure and the 12 sets of quaternionic units each set obeying the dicylic group structure of order 12 this fact is used to prove that the automorphism group of the octonionic root system of e7 is the finite subgroup of g2 of order 12 096 an explicit 7 7 matrix realization of which is constructed possible use of the octonionic representation of the e6 root system as orbifolds and the relevance of the binary tetrahedral structures with the statistical mechanics models are suggested

non existence of off critical yang baxter solutions for exceptional lie algebra models it is shown that pasquier s solution 1987 of the yang baxter equations for the models based on the exceptional lie algebras e6 e7 e8 and their affine counterparts does not admit an off critical extension in the space of weights of the configurations that satisfy the adjacency conditions imposed by the dynkin diagram

boundary conditions and inversion indentities for solvable lattice models with a sublattice symmetry the transfer matrices of solvable lattice spin models are considered under general boundary conditions associated with the symmetry of the models it is shown how the full symmetry can be exploited for systems having a sublattice symmetry by considering an extended model where the states distinguish the sublattices in this extended scheme the parity of the number of sites is tied to the boundary conditions the inversion identities can be extended and be used to obtain the full operator content of the critical models as an application the complete spectra of the transfer matrices for the eight vertex model at the decoupling point are calculated

l p convergence rates of solutions for n dimensional quasilinear damped wave equation we realize the asymptotic profile for the solutions to the n dimensional quasilinear damped wave equation in the divergence form is the solution of the corresponding linear parabolic equation with special initial data and we further show the lp 1 p infinity in particular p 1 convergence rates to this linear asymptotic profile c 2013 elsevier inc all rights reserved

random surfaces on hard spheres the relation between mass m and size r for self avoiding random surfaces enclosing a hard sphere of radius r is examined it is suggested that m approximately r2f r r r with f proportional to the surface roughness these functions are investigated using experimental data and theoretical arguments

lp convergence rate to nonlinear diffusion waves for p system with damping abstract in this paper we study the p system with frictional damping and show that the solutions time asymptotically tend to the nonlinear diffusion waves governed by the classical darcy s law by introducing an approximate green function we obtain the optimal l p 2 p convergence rate of the solution which is a perturbation of the nonlinear diffusion wave to the hyperbolic system

exact solubility of the dn series the author shows that the dn series of a newly constructed set of models is completely integrable in particular the model described by d4 is a non critical extension of the three state self dual potts model

the crumpled state of some non equilibrium fractal surfaces the authors study how the three dimensional air or pythagorean distance r q q between two points q and q on a non equilibrium crumpled fractal surface cs with the topology of the plane transforms in the internal or geodesic distance x q q with probability p x r after the unfolding of the cs on a plane the probability distribution p x r governing this process is examined for the first time among other results they find that 1 the width of p x r diverges for r near the ensemble average radius r of the cs and 2 x approximately r13

decay properties of solutions to the cauchy problem for the damped wave equation with absorption abstract we consider the cauchy problem for the damped wave equation with absorption u t t u u t u p 1 u 0 t x r r n the behavior of u as t is expected to be the same as that for the corresponding heat equation t p 1 0 t x r r n which has the similarity solution w a t x with the form t 1 p 1 f x t depending on a lim x x 2 p 1 f x 0 provided that p is less than the fujita exponent p c n 1 2 n in this paper as a first step if 1 p p c n and the data u 0 u 1 x decays exponentially as x without smallness condition the solution is shown to decay with rates as t u t l 2 u t l p 1 u t l 2 o t 1 p 1 n 4 t 1 p 1 n 2 p 1 t 1 p 1 1 2 n 4 those of which seem to be reasonable because the similarity solution w a t x has the same decay rates as for the proof the weighted l 2 energy method will be employed with suitable weight similar to that in todorova and yordanov y todorova b yordanov critical exponent for a nonlinear wave equation with damping j differential equations 174 2001 464 489

integrable and conformal boundary conditions for widehat s ell 2 a d e lattice models and unitary minimal conformal field theories integrable boundary conditions are studied for critical a d e and general graph based lattice models of statistical mechanics in particular using techniques associated with the temperley lieb algebra and fusion a set of boundary boltzmann weights which satisfies the boundary yang baxter equation is obtained for each boundary condition when appropriately specialized these boundary weights each of which depends on three spins decompose into more natural two spin edge weights the specialized boundary conditions for the a d e cases are naturally in one to one correspondence with the conformal boundary conditions of widehat s ell 2 unitary minimal conformal field theories supported by this and further evidence we conclude that in the continuum scaling limit the integrable boundary conditions provide realizations of the complete set of conformal boundary conditions in the corresponding field theories

dn models local densities the author computes the local densities of the dn series whose integrability was shown in a previous letter see ibid vol 20 no 4 p l217 20 1987

large time behavior of solutions for the nonlinear wave equation with viscosity in odd dimensions abstract we study the dissipation of solutions of the cauchy problem for the nonlinear dissipative wave equation in odd multi spatial dimensions pointwise estimates of the time asymptotic shape of the solutions are obtained and shown to exhibit the generalized huygens principle our approach is based on the detailed analysis of the green function of the linearized system this is used to study the coupling of nonlinear diffusion waves

protein chain packing and percolation threshold abstract the major factor that drives a protein chain toward collapse and folding is the hydrophobic effect amino acids with apolar side chains join forming a solvent shielded hydrophobic core this process pack the structure in the native one here we investigate the average packing density of 5526 protein chains deposited in the brookhaven protein data bank this analysis is carried out from the scaling analysis of the mass size exponent and it shows that the exponent is 2 47 this fractal dimension of the protein chain is close to the one obtained in the randomly packed spheres near their percolation threshold the present findings supply a measure of the protein compactness that tends to a constant protein chain packing the average packing density tends to 0 86 a u a3

global existence of solutions to 1 d euler equations with time dependent damping abstract in this paper we study the 1 d isentropic euler equations with time dependent damping our damping decays at a speed of order 1 with respect to time which is a little weaker than the linear one under our assumption we will prove the global existence of solutions to the euler system and obtain l 2 and l estimates for the solutions our approach is based on some detailed energy estimates

l1 l1 estimates for the strongly damped plate equation abstract in this paper we derive l 1 l 1 long time estimates for the strongly damped plate equation u t t 2 u 2 u t 0 x r n t r u 0 x u 0 x u t 0 x u 1 x in particular we prove that u t l 1 c 1 t n 4 u 0 l 1 1 t 1 2 u 1 l 1 for any t 0 in space dimension n 5

asymptotic behavior of solutions of quasilinear hyperbolic equations with linear damping we consider the asymptotic behavior of the solution of quasilinear hyperbolic equation with linear dampingvtt a vx x vt 0 x t r 0 subsequent to k nishihara j differential equations131 1996 171 188 in that article the system with dampingvt ux 0 ut p v x u p v 0 was treated and the convergence rates to the diffusion wave by l hsiao and t p liu comm math phys 143 1992 599 605 and l hsiao and t p liu chinese ann math ser b14 1993 465 480 were improved for initial data v0 u0 x satisfying v0 u0 v0 0 and v0 x v0 dx 0 this system is reduced to the quasilinear hyperbolic equation with linear dampingvtt p v0 vx p v0 x vt 0 and the decay rates v t l o t 1 2 vx t l o t 1 vt t l o t 3 2 were obtained provided that v vt t 0 h3 h2 is small and inl1 l1 from these decay rates vis expected to behave as a solution to the parabolic equation the aims of this paper are to seek the asymptotic profile x t satisfying t l o t 1 2 x t l o t 1 t t l o t 3 2 and to show that the solution of satisfies v t l o t 1 v x t l o t 3 2 v t t l o t 2 the proof is based on the elementary energy method and the green function method for the parabolic equation

global existence of small solutions to a class of nonlinear evolution equations on etudie le comportement global des solutions d une classe d equations d evolution non lineaires on considere le probleme aux valeurs initiales pour des equations quasilineaires qui sont des perturbations d equations lineaires dissipatives

global existence and optimal time decay estimates of solutions to the generalized double dispersion equation on the framework of besov spaces abstract we investigate the initial value problem for the generalized double dispersion equation in any dimensions inspired by 28 for the hyperbolic system of first order pdes we develop littlewood paley pointwise energy estimates for the dissipative wave equation of high order furthermore with aid of the frequency localization duhamel principle we establish the global existence and optimal decay estimates of solutions in spatially critical besov spaces our results could hold true for any dimensions n 1 indeed the proofs are different in case of high dimensions and low dimensions owing to interpolation tricks

decay estimates for dissipative wave equations in exterior domains abstract we study the exterior initial boundary value problem for the linear dissipative wave equation t u 0 in 0 with u t u t 0 u 0 u 1 and u 0 where is an exterior domain in n dimensional euclidean space r n we first show higher local energy decay estimates of the solution u t and then using the cut off technique together with those estimates we can obtain the l 1 estimate of the solution u t when n 3 that is u t l 1 c u 0 h n u 1 h n 1 u 0 w n 1 u 1 w n 1 1 for t 0 where n n 2 is the integer part of n 2 moreover by induction argument we derive the higher energy decay estimates of the solution u t for t 0

l p l q decay estimates for dissipative linear hyperbolic systems in 1d abstract given a b r n n we consider the cauchy problem for partially dissipative hyperbolic systems having the form t u a x u b u 0 with the aim of providing a detailed description of the large time behavior sharp l p l q estimates for 1 q p are established for the distance between the solution to the system and a time asymptotic profile where the profile is the superposition of diffusion waves and exponentially decaying waves they show that the solution to the system decays to the diffusion waves 1 2 faster than the diffusive decay rate 1 q 1 p 2 while the exponential decaying waves are negligible for large time in particular under a symmetry property it decays 1 faster than the proof is based on a complex interpolation argument once l r estimates for the fundamental solution to the system in the frequency space and fourier multiplier estimates are accomplished

large time behavior and lp lq estimate of solutions of 2 dimensional nonlinear damped wave equations abstract we show the asymptotic behavior of the solution to the cauchy problem of the two dimensional damped wave equation it is shown that the solution of the linear damped wave equation asymptotically decompose into a solution of the heat and wave equations and the difference of those solutions satisfies the lp lq type estimate this is a two dimensional generalization of the three dimensional result due to nishihara math z 244 2003 631 to show this we use the fourier transform and observe that the evolution operators of the damped wave equation can be approximated by the solutions of the heat and wave equations by using the lp lq estimate we also discuss the asymptotic behavior of the semilinear problem of the damped wave equation with the power nonlinearity u u our result covers the whole super critical case 1 where the 1 is well known as the fujita exponent when n 2

existence and nonexistence of time global solutions to damped wave equation on half line on the half line r 0 infinity the initial boundary value problems with null dirichlet boundary for both the semilinear heat equation and damped wave equation are considered the critical exponent p c n k of semilinear term for the existence and nonexistence about the semilinear heat equation on the halved space d n d k r k rn k is given by p c n k 1 2 n k j appl math phys 39 1988 135 149 arch rational mech anal 109 1990 63 71 since the damped wave equation is expected to be close to the heat equation j differential equations 191 2003 445 469 math z 244 2003 631 649 the critical exponent for the semilinear damped wave equation is expected to be same as that of the semilinear heat equation however there is no blow up result on the halved space for the damped wave equation in this paper the exponent pc l 1 2 is shown to be critical for the existence and nonexistence of time global solution to both the semilinear heat equation and damped wave equation on the half line r together with the derivation of the blow up time for the proof the explicit formulas of solutions are used in a similar fashion to those in li and zhou discrete continuous dynamic systems 1 1995 503 520 c 2005 elsevier ltd all rights reserved

exact representation of the asymptotic drift speed and diffusion matrix for a class of velocity jump processes abstract this paper examines a class of linear hyperbolic systems which generalizes the goldstein kac model to an arbitrary finite number of speeds v i with transition rates i j under the basic assumptions that the transition matrix is symmetric and irreducible and the differences v i v j generate all the space the system exhibits a large time behavior described by a parabolic advection diffusion equation the main contribution is to determine explicit formulas for the asymptotic drift speed and diffusion matrix in term of the kinetic parameters v i and i j establishing a complete connection between microscopic and macroscopic coefficients it is shown that the drift speed is the arithmetic mean of the velocities v i the diffusion matrix has a more complicate representation based on the graph with vertices the velocities v i and arcs weighted by the transition rates i j the approach is based on an exhaustive analysis of the dispersion relation and on the application of a variant of the kirchoff s matrix tree theorem from graph theory

local existence and uniqueness for a semilinear accretive wave equation abstract we study local existence and uniqueness in the phase space h h 1 r n of the solution of the semilinear wave equation u t t u u t u t p 1 for p 1

lp lq estimates of solutions to the damped wave equation in 3 dimensional space and their application it has been asserted that the damped wave equation has the diffusive structure as t in this paper we consider the cauchy problem in 3 dimensional space for the linear damped wave equation and the corresponding parabolic equation and obtain the lp lq estimates of the difference of each solution which represent the assertion precisely explicit formulas of the solutions are analyzed for the proof the second aim is to apply the lp lq estimates to the semilinear damped wave equation with power nonlinearity if the power is larger than the fujita exponent then the time global existence of small weak solution is proved and its optimal decay order is obtained

experimental study of the roughness of crumpled surfaces abstract we report on the experimental study of the roughness of randomly crumpled surfaces which are unfolded this system provides a natural example of random surfaces which exhibit long range correlations it is shown that such rough surfaces are self affine with a hurst exponent h 0 9 a simple one dimensional model illustrates the way long range correlations may naturally occur in the crumpling process

existence and nonexistence of global solutions for a nonlinear hyperbolic system with damping abstract this paper concerns with the cauchy problem for the damped nonlinear hyperbolic system u t t u u t v p t x r 1 r n v t t v v t u q t x r 1 r n u 0 x u 0 x u t 0 x u 1 x x r n v 0 x v 0 x v t 0 x v 1 x x r n where p q 1 and satisfy p q 1 we shall prove that if max 1 p p q 1 1 q p q 1 n 2 for n 1 or 3 then the solution with small initial data exists globally in time and satisfies the decay estimates u t c 1 t and v t c 1 t for some positive constants and while if max 1 p p q 1 1 q p q 1 n 2 for n 1 then every solution with initial data having positive average value does not exist globally

remarks on the asymptotic behavior of the solution to damped wave equations abstract we study the diffusion phenomena for damped wave equations we prove that the solution of an abstract damped wave equation becomes closer to the solution of a heat type equation as time tends to infinity under some assumption to the resolvent as an application of our approach we also study the asymptotic behavior of the damped wave equation in euclidean space under the geometric control condition

diffusion phenomenon for linear dissipative wave equations in an exterior domain abstract under the general condition of the initial data we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain in order to derive the diffusion phenomenon for dissipative wave equations the time integral method which was developed by ikehata and matsuyama sci math japon 55 2002 33 plays an effective role

on l1 estimates for solutions of dissipative wave equations abstract we consider the cauchy problem for the dissipative wave equation t u 0 in r n 0 with u t u t 0 u 0 u 1 in r n where t t 2 t x is the dissipative wave operator with laplacian x we derive the representation formulas in any dimension of the solution u u x t and then we obtain the l 1 estimates of the solution u t for any t 0 without any weighted conditions on the initial data u 0 u 1

wave equations with strong damping in hilbert spaces abstract we study the cauchy problem for abstract dissipative equations in hilbert spaces generalizing wave equations with strong damping terms in r n or exterior domains our main result is a generalized diffusion phenomenon the long time asymptotics of strongly damped wave equations is a combination of solutions of diffusion and wave equations in particular we obtain sharp decay estimates the proofs rely on the energy method in the fourier space and its generalization based on the spectral theorem for self adjoint operators

diffusion phenomena for partially dissipative hyperbolic systems abstract we consider a partially dissipative hyperbolic system with time dependent coefficients and show that under natural assumptions its solutions behave like solutions to a parabolic problem modulo terms of faster decay this generalises the well known diffusion phenomenon for damped waves and gives some further insights into the structure of dissipative hyperbolic systems

geometrical and electrical properties of crumpled wires geometrical and electrical properties of crumpled wires are investigated power laws connecting the geometrical and electrical properties of these random systems are studied and critical exponents are calculated in particular the authors have obtained the resistance exponent zeta which seems to be compatible with a previous conjecture

global existence and nonexistence of solutions for a system of nonlinear damped wave equations abstract we consider the cauchy problem for the system of semilinear damped wave equations with small initial data t 2 u 1 u 1 t u 1 u k p 1 t 0 x r n t 2 u 2 u 2 t u 2 u 1 p 2 t 0 x r n t 2 u k u k t u k u k 1 p k t 0 x r n u j 0 x a j x t u j 0 x b j x x r n 1 j k we show that a critical exponent which classifies the global existence and the finite time blow up of solutions indeed coincides with the one to a corresponding semilinear heat systems with small data the proof of the global existence is based on the l p l q estimates of fundamental solutions for linear damped wave equations k nishihara l p l q estimates of solutions to the damped wave equation in 3 dimensional space and their application math z 244 2003 631 649 k marcati p nishihara the l p l q estimates of solutions to one dimensional damped wave equations and their application to compressible flow through porous media j differential equations 191 2003 445 469 t hosono t ogawa large time behavior and l p l q estimate of 2 dimensional nonlinear damped wave equations j differential equations 203 2004 82 118 t narazaki l p l q estimates for damped wave equations and their applications to semilinear problem j math soc japan 56 2004 585 626 and the blow up is shown by the fujita kaplan zhang method q zhang a blow up result for a nonlinear wave equation with damping the critical case c r acad sci paris 333 2001 109 114 f sun m wang existence and nonexistence of global solutions for a nonlinear hyperbolic system with damping nonlinear anal 66 12 2007 2889 2910 t ogawa h takeda non existence of weak solutions to nonlinear damped wave equations in exterior domains nonlinear anal 70 10 2009 3696 3701

new exactly solvable orbifold models the author employs an orbifold procedure to construct new exactly solvable lattice statistical mechanical models starting with the su 3 models at level k 3j with j an integer he obtains new models with the same bulk free energy the bulk free energy is known for the su n models in a two parameter subspace of the full parameter space so the new models are also exactly solvable in this subspace he expresses the toroidal partition function of the original model as a sum over partition functions of the orbifold model with twisted boundary conditions each model has a critical point described by a conformal field theory with central charge c 2 1 12 k 3 k 2