拟线性抛物方程的熄灭(quenching)现象

本文研究一类带奇异项的拟线性抛物方程的初边值问题．得到了古典解的熄灭现象，并对熄灭解的渐近行为作了分析，包含了［２－５］的相应结论     

退缩抛物型方程解的熄灭时间

证明了一类退缩抛物型方程解在有限时刻熄灭,并对解的熄灭时间进行估计     

Quenching Time Estimates for Semilinear Parabolic Equations Controlled by Two Absorption Sources in Control System

This paper deals with the quenching solution of the initial boundary value problem for aclass of semilinear reaction-diffusion equation controlled by two absorption sources in control system and estimate upper bound and lower bound of the quenching time. We point that the number of absorption sources influences the time of quenching phenomenon.The solution can solve some boundary value problem in control system.     

The boundary quenching behavior of a semilinear parabolic equation

In this paper we consider the boundary quenching behavior of a semilinear parabolic problem in one-dimensional space, of which the nonlinearity appears both in the source term and in the Neumann boundary condition. First we proved that the solution quenches at somewhere in some finite time. Then we assert that the quenching can only occur on the left boundary if the given initial datum is monotone. Finally we derived the upper and lower bounds for the quenching rate of the solution near the quenching time. Thus we generalized our former results.     

Non-simultaneous quenching for a slow diffusion system coupled at the boundary

This paper deals with the quenching behavior of positive solutions to the Newton filtration equations coupled with boundary singularities.We determine quenching rates for nonsimultaneous quenching at f...     

Local and non‐local boundary quenching

The quenching problem is examined for a one‐dimensional heat equation with a non‐linear boundary condition that is of either local or non‐local type. Sufficient conditions are derived that establish both quenching and non‐quenching behaviour. The growth rate of the solution near quenching is also given for a power‐law non‐linearity. The analysis is conducted in the context of a nonlinear Volterra integral equation that is equivalent to the initial–boundary value problem. Copyright © 1999 John Wiley & Sons, Ltd.     

Critical Quenching Exponents for Heat Equations Coupled with Nonlinear Boundary Flux

We discuss the quenching phenomena for a system of heat equations coupled with nonlinear boundary flux. We determine a critical value for the exponents in the boundary flux, such that only in the super critical case the simultaneous quenching can happen for any solution.     

The fresh-salt water interface in a semi-pervious aquifer

The paper determines the location of the steady state interface between fresh and saltwater in a plane coastal aquifer. The lower boundary is totally impervious while the upper one is impervious below land and semi-pervious below the sea allowing an outflow through this part of the upper boundary. The model equations reduce to two boundary value problems, one valid in x < 0 and the other in x > 0 here x is measured along the aquifer with the origin at the coast. In each region unknown boundaries have to be determined as part of the solution using boundary and continuity conditions. Two cases are presented using the Dupuit approximation. One where the solution can be written down in terms of elementary functions and the other in which we have to use a phase space analysis.     

Quenching rates for heat equations with coupled singular nonlinear boundary flux

We study finite time quenching for heat equations coupled via singular nonlinear bound-ary flux. A criterion is proposed to identify the simultaneous and non-simultaneous quenchings. In particular, three kinds of simultaneous quenching rates are obtained for different nonlinear exponent re-gions and appropriate initial data. This extends an original work by Pablo, Quir′os and Rossi for a heat system with coupled inner absorption terms subject to homogeneous Neumann boundary conditions.     

Mixed boundary value problem for some pairs of metaanalytic function and analytic function

In this article, some mixed boundary value problems (BVPs) on the unit circumference for some pairs of a metaanalytic function and an analytic function are discussed. Using the relationship between metaanalytic function and polyanalytic function, the expression of solution and the condition of solvability for the problem are obtained by reducing the problem to an equivalent system of a Haseman BVP for analytic function and a Hilbert BVP for analytic function. Copyright © 2008 John Wiley & Sons, Ltd.     

On quenching for some parabolic problems with combined power-type nonlinearities

In this paper, we investigate initial-boundary value problems for nonlinear parabolic differential equations with combined power-type nonlinearities. We show that the solution of the above problem quenches in a finite time, and estimate its quenching time. Finally, we have carried out numerical experiments.     

带平方根的Hilbert边值问题

讨论了如下型Re{λ(t)√ψ (t)}=c(t),t∈L,的Hilbert边值问题，其中L是单位圆，λ(t)≠0与c(t)为Holder连续函数，ψ^ (t)在圆内全纯，在L上有单值连续的边值√ψ^ (t)，获得了其一般解和可解条件。     

Generalization of Backward Differentiation Formulas for Parallel Computers

We analyze an extension of backward differentiation formulas, used as boundary value methods, that generates a class of methods with nice stability and convergence properties. These methods are obtained starting from the boundary value GBDFs class, and are in the class of EBDF-type methods. We discuss different ways of using these linear multistep formulas in order to have efficient parallel implementations. Numerical experiments show their effectiveness.     

On the existence of bubble-type solutions of nonlinear singular problems

Considered in this paper is a class of singular boundary value&nbsp;problem, arising&nbsp;in hydrodynamics and nonlinear field theory, when centrally bubble-type solutions are&nbsp;sought: \((p(t)u0)0 = c(t)p(t)f(u); u0(0) = 0; u(+1) = L &gt; 0\) in the half-line \([0;+1)\), where \(p(0) = 0\). We are interested in strictly increasing solutions&nbsp;of this problem in \([0;1)\) having just one zero in \((0;+1) \)and finite limit at zero, which has&nbsp;great importance in applications or pure and applied mathematics. Su&plusmn;cient conditions&nbsp;of the existence of such solutions are obtained by applying the critical point theory and&nbsp;by using shooting argument [9,10] to better analysis the properties of certain solutions&nbsp;associated with the singular di&reg;erential equation. To the authors' knowledge, for the first&nbsp;time, the above problem is dealt with when f satis&macr;es non-Lipschitz condition. Recent&nbsp;results in the literature are generalized and signi&macr;cantly improved.     

A BOUNDARY ELEMENT METHOD FOR A NONLINEAR BOUNDARY VALUE PROBLEM IN STEADY-STATE HEAT TRANSFER IN DIMENSION THREE

In this paper, a new method of boundary reduction is proposed, which reduces thesteady-state heat transfer equation with radiation. Moreover, a boundary element method is pre-sented for its solution and the error estimates of the numerical approximations are given.     

Numerical quenching of a system of equations coupled at the boundary

We study numerical approximations of solutions of the following system of heat equations, coupled at the boundary through a nonlinear flux: where p and q are parameters. We prove that the solutions of a semidiscretization in space quench in finite time. Moreover, we describe in terms of p and q the simultaneous versus non‐simultaneous quenching phenomena. We also find the numerical extinction sets. Finally, in order to obtain the correct quenching rates in the non‐simultaneous case we present some adaptive methods. Copyright © 2009 John Wiley & Sons, Ltd.     

一类Dirichlet边值逆问题

给出解析函数的一类Dirichlet边值逆问题的数学提法.依据解析函数Dirichlet边值问题和广义Dirichlet边值问题的理论,讨论了此边值逆问题的可解性.利用解析函数Dirichlet边值问题的Schwarz公式,给出了该边值逆问题的可解条件和解的表示式.     

Generalized Stokes resolvent equations in an infinite layer with mixed boundary conditions

In this paper we prove unique solvability of the generalized Stokes resolvent equations in an infinite layer Ω₀ = ℝ^{n –1} × (–1, 1), n ≥ 2, in L^q ‐Sobolev spaces, 1 < q < ∞, with slip boundary condition of on the “upper boundary” ∂Ω⁺₀ = ℝ^{n –1} × {1} and non‐slip boundary condition on the “lower boundary” ∂Ω^–₀ = ℝ^{n –1} × {–1}. The solution operator to the Stokes system will be expressed with the aid of the solution operators of the Laplace resolvent equation and a Mikhlin multiplier operator acting on the boundary. The present result is the first step to establish an L^q ‐theory for the free boundary value problem studied by Beale [9] and Sylvester [22] in L ²‐spaces. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Dirichlet boundary value problems for p-Schrödinger operators on finite networks

In this paper, we define the discrete p-Schrödinger operators on finite networks and discuss the existence of the Dirichlet eigenvalues and their eigenfunctions for the operators. We also provide various equivalent conditions for the existence of positive solutions for Dirichlet boundary value problems for the operators.