Periodic Solutions of Porous Medium Equations with Weakly Nonlinear Sources

In this paper, we show the existence of the time periodic solutions to the porous medium equations of the formut= Δ (|u| m-1 u)+B(x,t,u)+f(x,t) in Ω×Rwith the Dirichlet boundary value condition, where m>1, Ω is a bounded domain in R N with smooth boundary Ω , the continuous function f and the Hlder continuous function B(x,t,u) are periodic in t with period ω and the nonlinear sources are assumed to be weaker, i.e., B(x,t,u) u≤b 0|u| α+1 with constants b 0≥0 and 0≤α<m.

SOLITARY WAVE AND PERIODIC WAVE SOLUTIONS FOR THE NON-NEWTONIAN FILTRATION EQUATIONS WITH NONLINEAR SOURCES AND A TIME-VARYING DELAY

This paper is concerned with the non-Newtonian filtration equations with non- linear sources and a time-varying delay. By an extension of Mawhin＇s continuation theorem and some analysis methods, several sufficient conditions ensuring the existence of solitary wave and periodic wave solutions are obtained. Some corresponding results in the literature are improved and extended. An example is given to illustrate the effectiveness of our results.

A Class of Cauchy Problems for Porous Medium Equations with Strongly Nonlinear Sources and Convections

In this paper we study existence of solutions of a class of Cauchy problems for porous medium equations with strongly nonlinear sources or absorptions and convections when the initial trace is a Radon measure μ on RN.

On the Cauchy problem for a doubly nonlinear degenerate parabolic equation with strongly nonlinear sources

In this article, we consider the existence of local and global solution to the Cauchy problem of a doubly nonlinear equation. By introducing the norms |||f||| h and 〈f〉h, we give the sufficient and necessary conditions on the initial value to the existence of local solution of doubly nonlinear equation. Moreover some results on the global existence and nonexistence of solutions are considered.

A Note to the Cauchy Problem for the Degenerate Parabolic Equations with Strongly Nonlinear Sources

In this note we study the nonexistence of nontrivial global solutions on S = R^N × （0,∞） for the following inequalities：｜u｜t≥△（｜u｜^m-1u）＋｜u｜^q and ｜u｜t≥div（｜△u｜^p-2△｜u｜）＋｜u｜^q.When m,p,q satisfy some given conditions, the nonexistence of nontrivial global solution is proved, without taking their traces on the hyperplans t = 0 into account.

Thermodynamics and phase transition of topological dS black holes with a nonlinear source

We discuss black hole solutions of Einstein-Λ gravity in the presence of nonlinear electrodynamics in dS spacetime.Considering the correlation of the thermodynamic quantities respectively corresponding to the black hole horizon and cosmological horizon of dS spacetime and taking the region between the two horizons as a thermodynamic system,we derive effective thermodynamic quantities of the system according to the first law of thermodynamics,and investigate the thermodynamic properties of the system under the influence of nonlinearity parameter α.It is shown that nonlinearity parameter α influences the position of the black hole horizon and the critical state of the system,and along with electric charge has an effect on the phase structure of the system,which is obvious,especially as the effective temperature is below the critical temperature.The critical phase transition is proved to be second-order equilibrium phase transition by using the Gibbs free energy criterion and Ehrenfest equations.

The Velocity Measurement of Two-phase Flow Based on Particle Swarm Optimization Algorithm and Nonlinear Blind Source Separation

In order to overcome the disturbance of noise,this paper presented a method to measure two-phase flow velocity using particle swarm optimization algorithm,nonlinear blind source separation and cross correlation method.Because of the nonlinear relationship between the output signals of capacitance sensors and fluid in pipeline,nonlinear blind source separation is applied.In nonlinear blind source separation,the odd polynomials of higher order are used to fit the nonlinear transformation function,and the mutual information of separation signals is used as the evaluation function.Then the parameters of polynomial and linear separation matrix can be estimated by mutual information of separation signals and particle swarm optimization algorithm,thus the source signals can be separated from the mixed signals.The two-phase flow signals with noise which are obtained from upstream and downstream sensors are respectively processed by nonlinear blind source separation method so that the noise can be effectively removed.Therefore,based on these noise-suppressed signals,the distinct curves of cross correlation function and the transit times are obtained,and then the velocities of two-phase flow can be accurately calculated.Finally,the simulation experimental results are given.The results have proved that this method can meet the measurement requirements of two-phase flow velocity.

GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO A NONLOCAL EVOLUTION p-LAPLACE SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS

In this paper, the authors discuss the global existence and blow-up of the solution to an evolution p-Laplace system with nonlinear sources and nonlinear boundary condition. The authors first establish the local existence of solutions, then give a necessary and sufficient condition on the global existence of the positive solution.

An Explicit Lower Bound for Blow Up Time in a Class of Nonlinear Wave Equations with Nonlinear Damping and Source Terms

This paper deals with an initial boundary value problem for a class of nonlinear wave equation with nonlinear damping and source terms whose solution may blow up in finite time.An explicit lower bound for blow up time is determined by means of a differential inequality argument if blow up occurs.

Study of the second harmonic sound field from a circular piston source and the influence in the nonlinearity parameter tomography

In the nonlinearity parameter B/A tomography using the second harmonic wav, it is very important to analyze the ultrasonic field of the transducer, especially the generation of the second harmonic wave in the nearfield. In this paper, the theoretical study and experimental measurements of the second harmoinc pressure field from a circular piston source are performed.And the effect on the nonlinearity parameter tomograaphy is discussed. The results will be used to decrease the error of reconstruction in nonlinearity parameter tomography and bring the ultrasoinc diagnosis a step forward

COMPARISON OF LINEAR AND NONLINEAR WAVES ASSOCIATED WITH STEADY-STATE FORCING SOURCES

Low-frequency phenomena in the atmosphere are intimately related to stationary waves and, in a sense, the former may even be viewed as the time-varying part of the quasi-stationary waves themselves, Much attention has been focused on nonlinear interactions in the conceptual study on stationary waves. Linear and nonlinear primitive-equation baroclinic spectral models are adopted to investigate the response of stationary waves to large- scale mechanical forcing and steady-state thermal forcing, both idealized and realistic, followed by calculations of the EP fluxes and three-dimensional wave activity fluxes (Plumb, 1985) for both the linear and nonlinear solu- tions. Results show that when the forcing source grows intense enough to be comparable to the real one, non- linear interaction becomes very important, especially for the maintenance of tropical and polar stationary waves. Care should be taken, however, in using the EP flux and Plumb's 3-D flux for diagnostic analysis of observational data as they are highly sensitive to nonlinear interaction.

Propagations of singularities in a parabolic system with coupling nonlocal sources

This paper deals with propagations of singularities in solutions to a parabolic system coupled with nonlocal nonlinear sources. The estimates for the four possible blow-up rates as well as the boundary layer profiles are established. The critical exponent of the system is determined also.

RESTRICTED ADDITIVE SCHWARZ METHOD FOR A KIND OF NONLINEAR COMPLEMENTARITY PROBLEM

In this paper, a new Schwarz method called restricted additive Schwarz method （RAS） is presented and analyzed for a kind of nonlinear complementarity problem （NCP）. The method is proved to be convergent by using weighted maximum norm. Besides, the effect of overlap on RAS is also considered. Some preliminary numerical results are reported to compare the performance of RAS and other known methods for NCP.

BLOW-UP RATE OF SOLUTIONS FOR P-LAPLACIAN EQUATION

In this note we consider the blow-up rate of solutions for p-Laplacian equation with nonlinear source, ut = div（｜↓△u｜p-2↓△u）＋uq, （x, t） ∈ RN × （0, T）, N ≥ 1. When q 〉 p - 1, the blow-up rate of solutions is studied.