[PDF] Top 20 Asymptotic behavior of the solutions of a discrete reaction diffusion equation

... Introduction. Discrete reaction-diffusion type partial difference equations have recently been introduced by a number of authors as models for the study of spatio- temporal chaos ...and asymptotic ... See full document

... viscosity solutions with asymptotic behavior of the parabolic Monge-Ampère equation ...multi-valued solutions with prescribed asymptotic be- havior at ... See full document

... complicated asymptotic behavior of solutions for the Cauchy problem of the evolution p-Laplacian equation with ...complicated asymptotic behavior of the ... See full document

... the asymptotic behavior of nontriv- ial nonnegative solutions of the initial boundary value problem ...the equation has periodic sources, it is of no meaning to consider the steady ...periodic ... See full document

... a trivial Carnot group. In the Euclidean case, we first recall that Zhang [] studied the global existence for a parabolic problem in divergence form analogous to (.) when the potential V is in parabolic Kato class at ... See full document

... continuous functions fs, g s, and hs defined for s ∈ R. The function gs is assumed monotone. The paper 11, 12 proves the existence and uniqueness of both local and global solutions of this system on the finite ... See full document

... -periodic solutions for λ ∈ (, λ ∗ ) and does not have any positive T -periodic solutions for λ > λ ∗ , where a(n), h(n), and τ (n) are T-periodic ...periodic solutions to a class of functional ... See full document

... Abstract. The Cauchy problem for the damped Boussinesq equation with small initial data is considered in two space dimensions. Existence and uniqueness of its classical so- lution is proved and the solution is ... See full document

... that solutions with negative initial energy blow up in finite ...that solutions with negative energy continue to exist globally in time t if q ≥ r and blow up in finite time if q < r and the initial ... See full document

... A supersolution [or subsolution] is similarly defined with equality of (.) replaced by ≥ [or ≤]. The weak solutions for problem (.)-(.) can be defined in a similar way as above. It is well known that problem ... See full document

... the asymptotic behavior of the nonnegative solutions of the initial boundary value ...periodic solutions from the upper bound according to the maximum ...the asymptotic boundedness of ... See full document

... wave solutions to a spatially-discrete diffusion equation with cubic nonlinearity on a one-dimensional integer ...the equation studied herein are well established (see ...in ... See full document

... Burgers equation and solve the initial value problem for ...the asymptotic behavior of solutions and we show that the exact solution of boundary value prob- lem for viscid Burgers ... See full document

... the asymptotic com- pactness of solutions cannot be obtained by the usual ...the asymptotic behavior of nonautonomous wave equa- tions, they prove that the family of processes is uniformly ... See full document

... In this paper, we not only give the asymptotic behavior at the origin for the maximum modulus of weak solutions of the stationary Schrödinger equation in a cone but also obtain the prope[r] ... See full document

... By a change of variables with cut-off functions, we study the existence and the asymptotic behavior of positive solutions for a general quasilinear Schrödinger equation which arises from plasma ... See full document

... numerical solutions of boundary value problems of partial differential equations often use a variety of finite difference or finite element formulations of differential equations, it is also quite common to convert ... See full document

... diffusion equation (not of neutral type) with non-monotone reaction, we firstly cite the paper by Ma ...sion equation (3) with non-monotone function f by constructing two auxiliary equations with ... See full document

... the asymptotic behavior (for ) of solutions of the Cauchy problem for a nonlinear parabolic equation with a double nonlinearity, describing the diffusion of heat with nonlinear heat ... See full document

... Motivated by the above mentioned works, the aim of this paper is threefold. First, we de- termine optimal conditions for the existence and nonexistence of global solutions to (.). Secondly, by using the scaling ... See full document