In this paper, the nonlinear wave equation u tt +bu t= Δ u+F(u), t>0,x∈R 3, u(0,x)=f(x), u t(0,x)=g(x) is discussed, where Δ = ∑3i=1 2x 2 i, b>0. The existence of global solution for this equation is obtained.
In biological study,Gierer and Meinhardt set the following re-action-diffusion equations u_t=d△u-μu+u_r/v~q+σ_1 v_t=D△v-vu+u~r/v~s+σ_2The existence of Global solution is proved by upper and lower solutions. Themain conclusions from Wu Jianhua are improved and popularized.
The existence of global solution and periodic solution is discussed for nonlinear evolution equation u′(t)+Au(t)=f(t,u(t)) in an ordered Banach space X ,where A is a closed linear operator in X and - A generates a C 0 semigroup T(t),f:×X→X only satisfies weak Carathéodory condition.
In this paper,the long thme behavior of solution for B-BBM equation with periodic boundary condition:ut-δ 3ux 2t-α 2ux 2+g(u) x+γu=f(x) is studied. The existence uniqueness of solution,existence of global attractor for the above problem are proved.
本文研究了周期边界条件下B BBM方程 : u t-δ 3 u x2 t-α 2 u x2 +g(u) x+γu=f(x)的长时间动力学行为 ,证明了该方程组的存在唯一性的整体吸引子的存在性
Through an analysis of the fundamental theory of scattered light holopho- toelasticity, the paper points out that the main difficulty concerning this topic is the simultaneous existence of global optical effects in all paths. Moreover, there exist at the same time speckle and photoelastic effects. For materials that are not photoelastically sensitive(such as plexiglass),the speckle effect is the main problem.
In this Paper we shall discuss the non-existence of global solution ofinitial boundary Value problems for a class semilinear parabiolic equationWe have obtained three theorems and partly solved the problems arisng,from the paper of C. V. pao.
In this article, We consider the quenching problem for quasi-linear parabolic Systms. As a model, We consider the following initial-boundary Value problem Where Ω is a bounded open set in R~n, D≡(0 ,T)×Ω,Γ=(0,T)×(?), 0=B. Conditions under which quenching occurs in finite time and the condition for the existence of global solution are given.