Existence,uniqueness and convergence as vanishing viscosity for a reaction-diffusion-convection system

A simple qualitative model of dynamic combustion

Brownian motion with negative drift and convex level sets in space-time

Suppose a, b, and are reals witha<b and consider the following diffusion equation

Probabilistic approach to the Dirichlet problem of second order elliptic PDE

In this paper we provide a probabilistic approach to the following Dirichlet Problem{(∑x~4(α~(ij) x~j) ∑b~ix~i ξ)u=0, iD u=g, on D,without assuming that the eigenvalues of the operator∑x~i(α~(ij)x~j) ∑b~ix~i ξwith Dirichlet boundary conditions are all strictly negative. The results of this paper generalizedthose of Ma.     

The critical exponent for a weakly coupled system of the generalized Fujita type reaction-diffusion equations

We study nonnegative solutions of the initial value problem for a weakly coupled system

Finite difference schemes of the nonlinear pseudo-parabolic system

ＦＩＮＩＴＥＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＳＯＦＴＨＥＮＯＮＬＩＮＥＡＲＰＳＥＵＤＯ－ＰＡＲＡＢＯＬＩＣＳＹＳＴＥＭＤＵＭＩＮＧＳＨＥＮＧ（杜明笙）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＰｈｙｓｉｃｓａｎｄＣｏｍｐｕｔａｔｉｏｎａｌＭａｔｈｅｍａｔ...     

Analytic solutions of differential-functional equations

We consider the general differential-functional equations

Analytic solution of vector model kinetic equations with constant kernel and their applications

Exact solutions are obtained for the first time for the half-space boundary-value problem for the vector model kinetic equations

Uniformly maldistributed sequences in a strict sense

It is shown that the following three limits

A semilinear parabolic system in a bounded domain

Consider the system

Concentration phenomena in weakly coupled elliptic systems with critical growth*

In this paper we consider the weakly coupled elliptic system with critical growth

Existence and asymptotic behaviour of solutions of a nonlinear evolution problem

We prove existence and asymptotic behaviour of a weak solutions of a mixed problem for where A is the pseudo-Laplacian operator.     

A predator-prey model with combined death and competition terms

The existence of a positive solution for the generalized predator-prey model for two species

Fourier-integral-operator product representation of solutions to first-order symmetrizable hyperbolic systems

We consider the first-order Cauchy problem

Numerical Approximation of a Reaction-Diffusion System with Fast Reversible Reaction

The authors consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction.It is deduced from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and satisfies estimates which do not depend on the kinetic rate.It follows that the solution converges to the solution of a nonlinear diffusion problem,as the size of the volume elements and the time steps converge to zero while the kinetic rate tends to infinity.     

Interlineation of functions of two variables on M(M>-2) lines preserving the class Cr(R2)

An algorithm for constructing the operator O_Mn({_kx}; x, y) with the properties

Low Regularity Solution of the Initial-Boundary-Value Problem for the ＂Good＂ Boussinesq Equation on the Half Line

we study an initial-boundary-value problem for the ＂good＂ Boussinesq equation on the half line
{δt^2u-δx^2u＋δx^4u＋δx^2u^2=0,t〉0,x〉0.
u（0,t）=h1（t）,δx^2u（0,t） =δth2（t）,
u（x,0）=f（x）,δtu（x,0）=δxh（x）.
The existence and uniqueness of low reguality solution to the initial-boundary-value problem is proved when the initial-boundary data （f, h, h1, h2） belong to the product space
H^5（R^＋）×H^s-1（R^＋）×H^s/2＋1/4（R^＋）×H^s/2＋1/4（R^＋）
1 The analyticity of the solution mapping between the initial-boundary-data and the with 0 ≤ s 〈 1/2. solution space is also considered.     

On the surjectivity of the almost linear operator and its applications

LetL be a self-adjoint linear operator andN be the gradient of a functional ϕ, which is almost quadratic. We first give a theorem on the surjectivity of the operatorL+N, then apply the result to semilinear elliptic systems:

On positive solutions of quasilinear elliptic systems

In this paper, we consider the existence and nonexistence of positive solutions of degenerate elliptic systems where –_p is the p-Laplace operator, p > 1 and is a C ^1,-domain in . We prove an analogue of [7, 16] for the eigenvalue problem with and obtain a non-existence result of positive solutions for the general systems.     

Generalized sine equations,II

In this paper we solve the equations

On the oscillation and asymptotic behavior of the solutions of a certain system of differential-functional equations of neutral type

Conditions for the oscillation of all solutions and for the existence of nonoscillatory solutions with polynomial growth at infinity are given for the system of differential-functional equations of neutral type