http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
BLOW UP OF SOLUTIONS WITH POSITIVE INITIAL ENERGY FOR THE NONLOCAL SEMILINEAR HEAT EQUATION
ZHONG BO FANG,LU SUN 한국산업응용수학회 2012 Journal of the Korean Society for Industrial and A Vol.16 No.4
In this paper, we investigate a nonlocal semilinear heat equation with homogeneous Dirichlet boundary condition in a bounded domain, and prove that there exist solutions with positive initial energy that blow up in finite time.
Negatively bounded solutions for a parabolic partial differential equation
Zhong Bo Fang,곽민규 대한수학회 2005 대한수학회보 Vol.42 No.4
In this note, we introduce a new proof of the uniqueness and existence of a negatively bounded solution for a parabolic partial differential equation. The uniqueness in particular implies the finiteness of the Fourier spanning dimension of the global attractor and the existence allows a construction of an inertial manifold.
NEGATIVELY BOUNDED SOLUTIONS FOR A PARABOLIC PARTIAL DIFFERENTIAL EQUATION
FANG ZHONG BO,KWAK, MIN-KYU Korean Mathematical Society 2005 대한수학회보 Vol.42 No.4
In this note, we introduce a new proof of the unique-ness and existence of a negatively bounded solution for a parabolic partial differential equation. The uniqueness in particular implies the finiteness of the Fourier spanning dimension of the global attractor and the existence allows a construction of an inertial manifold.
A NONLINEAR LIOUVILLE THEOREM IN HALF SPACE
ZHONG BO FANG,MINKYU KWAK 한국산업응용수학회 2006 Journal of the Korean Society for Industrial and A Vol.10 No.1
We prove a Liouville theorem of a semilinear elliptic equation: △u+f(xn, u)=0 defined in half space with zero boundary data, here n>2, f satisfies suitable conditions. In fact we show that if u is a nonnegative classical solution, then u becomes identically zero. The result was proved by using the moving plane method and by investigating an ordinary differential equation.
Complete classification of shape functions of self-similar solutions
Fang, Zhong Bo,Kwak, Minkyu Elsevier 2007 Journal of mathematical analysis and applications Vol.330 No.2
<P><B>Abstract</B></P><P>In this paper we study some asymptotic profiles of shape functions of self-similar solutions to the initial-boundary value problem with <I>Neumann</I> boundary condition for the generalized KPZ equation: <SUB>ut</SUB>=<SUB>uxx</SUB>−<SUP>|<SUB>ux</SUB>|q</SUP>, where <I>q</I> is positive number. The shapes of solutions of the corresponding nonlinear ordinary differential equation are of very different nature. The properties depend on the critical value q=1,32,2 and initial data as usual.</P>
LIOUVILLE THEOREMS OF SLOW DIFFUSION DIFFERENTIAL INEQUALITIES WITH VARIABLE COEFFICIENTS IN CONE
ZHONG BO FANG,CHAO FU,LINJIE ZHANG 한국산업응용수학회 2011 Journal of the Korean Society for Industrial and A Vol.15 No.1
We here investigate the Liouville type theorems of slow diffusion differential inequality and its coupled system with variable coefficients in cone. First, we give the definition of global weak solution, and then we establish the universal estimate ( does not depend on the initial value ) of solution by constructing test function. At last, we obtain the nonexistence of non-negative non-trivial global weak solution within the appropriate critical exponent. The main feature of this method is that we need not use comparison theorem or the maximum principle.
A VERY SINGULAR SOLUTION OF A DOUBLY DEGENERATE PARABOLIC EQUATION WITH NONLINEAR CONVECTION
Fang, Zhong Bo Korean Mathematical Society 2010 대한수학회지 Vol.47 No.4
We here investigate an existence and uniqueness of the nontrivial, nonnegative solution of a nonlinear ordinary differential equation: $$[\mid(w^m)]'\mid^{p-2}(w^m)']'\;+\;{\beta}rw'\;+\;{\alpha}w\;+\;(w^q)'\;=\;0$$ satisfying a specific decay rate: $lim_{r\rightarrow\infty}\;r^{\alpha/\beta}w(r)$ = 0 with $\alpha$ := (p - 1)/[pd-(m+1)(p-1)] and $\beta$:= [q-m(p-1)]/[pd-(m+1)(p-1)]. Here m(p-1) > 1 and m(p - 1) < q < (m+1)(p-1). Such a solution arises naturally when we study a very singular solution for a doubly degenerate equation with nonlinear convection: $$u_t\;=\;[\mid(u^m)_x\mid^{p-2}(u^m)_x]_x\;+\;(u^q)x$$ defined on the half line.