Oscillation Criteria for Second Order Mixed Nonlinear Elliptic Equations

By using the refinement of the standard integral averaging technique, we obtain some oscillation criteria for second order mixed nonlinear elliptic equations. The results established in this paper extend and improve some existing oscillation criteria for half-linear PDE in the literature.

ALGORITHM OF SOLUTIONS FOR MIXEDNONLINEAR VARIATIONAL-LIKE INEQUALITIES IN REFLEXIVE BANACH SPACE

In this paper, the author studies a class of mixed nonlinear variational-like inequalities in reflexive Banach space. By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solutions for the mixed nonlinear variational-like inequalities are proved. Next, by applying the auxiliary problem technique, rite author suggests an innovative iterative algorithm to compute the approximate solutions of the mixed nonlinear variational-like inequalities. Finally, the convergence criteria is also discussed.

Local regularity properties for ID mixed nonlinear Schrodinger equations on half-line

The main purpose of this paper is to consider the initial-boundary value problem for the 1D mixed nonlinear Schrodinger equation ut=iαu_(xx)+βu^(2)u_(x)+γ|u|^(2)u_(x)+i|u|^(2)u on the half-line with inhomogeneous boundary condition.We combine Laplace transform method with restricted norm method to prove the local well-posedness and continuous dependence on initial and boundary data in low regularity Sobolev spaces.Moreover,we show that the nonlinear part of the solution on the half-line is smoother than the initial data.

The Marginal Rao-Blackwellized Particle Filter for Mixed Linear/Nonlinear State Space Models

In this paper, the marginal Rao-Blackwellized particle filter （MRBPF）, which fuses the Rao-Blackwellized particle filter （RBPF） algorithm and the marginal particle filter （MPF） algorithm, is presented. The state space is divided into linear and non-linear parts, which can be estimated separately by the MPF and the optional Kalman filter. Through simulation in the terrain aided navigation （TAN） domain, it is demonstrated that, compared with the RBPF, the root mean square errors （RMSE） and the error variance of the nonlinear state estimations by the proposed MRBPF are respectively reduced by 29% and 96%, while the unique particle count is increased by 80%. It is also found that the MRBPF has better convergence properties, and analysis has shown that the existing RBPF is nothing more than a special case of the MRBPF.

Effectiveness of Darcy-Forchheimer and nonlinear mixed convection aspects in stratified Maxwell nanomaterial flow induced by convectively heated surface

The effect of nonlinear mixed convection in stretched flows of rate-type nonNewtonian materials is described. The formulation is based upon the Maxwell liquid which elaborates thermal relation time characteristics. Nanofluid properties are studied considering thermophoresis and Brownian movement. Thermal radiation, double stratification, convective conditions, and heat generation are incorporated in energy and nanoparticle concentration expressions. A boundary-layer concept is implemented for the simplification of mathematical expressions. The modeled nonlinear problems are computed with an optimal homotopy scheme. Moreover, the Nusselt and Sherwood numbers as well as the velocity, nanoparticle concentration, and temperature are emphasized. The results show opposite impacts of the Deborah number and the porosity factor on the velocity distribution.

OBLIQUE DERIVATIVE PROBLEMS FOR SECOND ORDER NONLINEAR MIXED EQUATIONS WITH DEGENERATE LINE

The present article deals with oblique derivative problems for some nonlinear mixed equations with parabolic degeneracy, which include the Tricomi problem as a special case. First, the formulation of the problems for the equations is given; next, the representation and estimates of solutions for the above problems are obtained; finally, the existence of solutions for the problems is proved by the successive iteration and the compactness principle of solutions of the problems. In this article, the author uses the complex method, namely, the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used.

THE MIXED PROBLEM FOR A CLASS OF NONLINEAR SYMMETRIC HYPERBOLIC SYSTEMS WITH DISCONTINUOUS DATA

This paper studies the nonlinear mixed problem for a class of symmetric hyperbolic systems with the boundary condition satisfying the dissipative condition about discontinuous data in higher dimension spaces, establishes the local existence theorem by using the method of a prior estimates, and obtains the structure of singularities of the solutions of such problems.

PERIODIC BOUNDARY VALUE PROBLEMS FOR NONLINEAR IMPULSIVEINTEGRODIFFERENTIAL EQUATIONS OF MIXED TYPE IN BANACH SPACES

In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.

UNIFORM BLOW-UP PROFILES FOR HEAT EQUATIONS WITH COUPLING NONLOCAL SOURCES OF ASYMMETRIC MIXED TYPE NONLINEARITIES

This article deals with a nonlocal heat system subject to null Dirichlet bound- ary conditions, where the coupling nonlocal sources consist of mixed type asymmetric non- linearities. We at first give the criterion for simultaneous blow-up of solutions, and then establish the uniform blow-up profiles of solutions near the blow-up time. It is observed that not only the simultaneous blow-up rates of the two components u and v are asymmet- ric, but also the blow-up rates of the same component u （or v） may be in different levels under different dominations.

A NONLINEAR LAVRENTIEV-BITSADZE MIXED TYPE EQUATION

In this paper the Tricomi problem for a nonlinear mixed type equation is studied. The coefficients of the mixed type equation are discontinuous on the line, where the equation changes its type. The existence of solution to this problem is proved. The method developed in this paper can be applied to study more difficult problems for nonlinear mixed type equations arising in gas dynamics.

APPROXIMATE SOLUTION TO A CLASS OF MULTIVALUED NONLINEAR MIXED VARIATIONAL INCLUSIONS

Concerned with the existence and convergence properties of approximate solution to multivalued nonlinear mixed variational inclusion problem in a Hilbert space, we established the equivalence between the variational inclusion and the general resolvent equations, obtained three iterative algorithms, provided the convergence analysis of the algorithms. The results obtained improve and generalize a number of resent results.

Responses of River Runoff to Climate Change Based on Nonlinear Mixed Regression Model in Chaohe River Basin of Hebei Province, China

Taking the nonlinear nature of runoff system into account,and combining auto-regression method and multi-regression method,a Nonlinear Mixed Regression Model (NMR) was established to analyze the impact of temperature and precipitation changes on annual river runoff process. The model was calibrated and verified by using BP neural network with observed meteorological and runoff data from Daiying Hydrological Station in the Chaohe River of Hebei Province in 1956–2000. Compared with auto-regression model,linear multi-regression model and linear mixed regression model,NMR can improve forecasting precision remarkably. Therefore,the simulation of climate change scenarios was carried out by NMR. The results show that the nonlinear mixed regression model can simulate annual river runoff well.

Darcy-Forchheimer flow with nonlinear mixed convection

An analysis of the mixed convective flow of viscous fluids induced by a nonlinear inclined stretching surface is addressed.Heat and mass transfer phenomena are analyzed with additional effects of heat generation/absorption and activation energy,respectively.The nonlinear Darcy-Forchheimer relation is deliberated.The dimensionless problem is obtained through appropriate transformations.Convergent series solutions are obtained by utilizing an optimal homotopic analysis method(OHAM).Graphs depicting the consequence of influential variables on physical quantities are presented.Enhancement in the velocity is observed through the local mixed convection parameter while an opposite trend of the concentration field is noted for the chemical reaction rate parameter.

A NONLINEAR GALERKIN/PETROV-LEAST SQUARES MIXED ELEMENT METHOD FOR THE STATIONARY NAVIER-STOKES EQUATIONS

A nonlinear Galerkin/Petrov-least squares mixed element (NGPLSME) method for the stationary Navier-Stokes equations is presented and analyzed. The scheme is that Petrov-least squares forms of residuals are added to the nonlinear Galerkin mixed element method so that it is stable for any combination of discrete velocity and pressure spaces without requiring the Babu*lka-Brezzi stability condition. The existence, uniqueness and convergence (at optimal rate) of the NGPLSME solution is proved in the case of sufficient viscosity (or small data).

A NONLINEAR GALERKIN MIXED ELEMENT METHOD AND A POSTERIORI ERROR ESTIMATOR FOR THE STATIONARY NAVIER-STOKES EQUATIONS

A nonlinear Galerkin mixed element (NGME) method and a posteriori error exstimator based on the method are established for the stationary Navier-Stokes equations. The existence and error estimates of the NGME solution are first discussed, and then a posteriori error estimator based on the NGME method is derived.

NONLINEAR GALERKIN MIXED ELEMENT METHODS FOR STATIONARY INCOMPRESSIBLE MAGNETOHYDRODYNAMICS

A nonlinear Galerkin mixed element （NGME） method for the stationary incompressible magnetohydrodynamics equations is presented. And the existence and error estimates of the NGME solution are derived.

Numerical solutions of two-dimensional nonlinear integral equations via Laguerre Wavelet method with convergence analysis

In this paper,the approximate solutions for two different type of two-dimensional nonlinear integral equations:two-dimensional nonlinear Volterra-Fredholm integral equations and the nonlinear mixed Volterra-Fredholm integral equations are obtained using the Laguerre wavelet method.To do this,these two-dimensional nonlinear integral equations are transformed into a system of nonlinear algebraic equations in matrix form.By solving these systems,unknown coefficients are obtained.Also,some theorems are proved for convergence analysis.Some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method.

THE PROBLEMS OF NONLINEAR BENDING FOR ORTHOTROPIC RECTANGULAR PLATE WITH FOUR CLAMPED EDGES

In this paper,under the non-uniformtransverse load,the problems of nonlinear bending for orthotropic rectangular plate are studied by using'the method of twovariable'[1]and 'the method of mixing perturbation'[2].The uniformly valid asymptotic solutions of Nth-order for ε1 and Mth-order for ε2 for ortholropic rectangular plale with four clamped edges are oblained.

Quantum plasmon enhanced nonlinear wave mixing in graphene nanoflakes

A distant-neighbor quantum-mechanical method is used to study the nonlinear optical wave mixing in graphene nanoflakes(GNFs),including sum-and difference-frequency generation,as well as four-wave mixing.Our analysis shows that molecular-scale GNFs support quantum plasmons in the visible spectrum region,and significant enhancement of nonlinear optical wave mixing is achieved.Specifically,the second-and third-order wave-mixing polarizabilities of GNFs are dramatically enhanced,provided that one(or more) of the input or output frequencies coincide with a quantum plasmon resonance.Moreover,by embedding a cavity into hexagonal GNFs,we show that one can break the structural inversion symmetry and enable otherwise forbidden second-order wave mixing,which is found to be enhanced by the quantum plasmon resonance too.This study reveals that the molecular-sized graphene could be used in the quantum regime for nanoscale nonlinear optical devices and ultrasensitive molecular sensors.

Three-dimensional nonlinear H_2/H_∞ guidance law based upon approach of solving the state feedback Nash balance point

Based upon the theory of the nonlinear quadric two-person nonzero-sum differential game,the fact that the time-limited mixed H2/H∞ control problem can be turned into the problem of solving the state feedback Nash balance point is mentioned. Upon this,a theorem about the solution of the state feedback control is given,the Lyapunov stabilization of the nonlinear system under this control is proved,too. At the same time,this solution is used to design the nonlinear H2/H∞ guidance law of the relative motion between the missile and the target in three-dimensional(3D) space. By solving two coupled Hamilton-Jacobi partial differential inequalities(HJPDI),a control with more robust stabilities and more robust performances is obtained. With different H∞ performance indexes,the correlative weighting factors of the control are analytically designed. At last,simulations under different robust performance indexes and under different initial conditions and under the cases of intercepting different maneuvering targets are carried out. All results indicate that the designed law is valid.