[PDF] Top 20 We study the following nonlinear parabolic equation:

... to the blow-up behaviours of solutions in order to understand the mechanism of thermal runway in combustion ...problem. We are interested in the global and non-global existence of positive ... See full document

... to the double time derivative on the right-hand side of ...Over the last twenty years, there has been a vast amount of research concerning the nonrelativistic limit of the Cauchy ... See full document

... to the conventional stable nonlinear Schro¨dinger 共SNLS, for short 兲 ...Since the SNLS equation has been proved to be a completely integrable system, 4,5 it has been solved by using the ... See full document

... u), the equation (1.2) is called Fisher’s equation [9] or KPP equation [11] which arises in the study of gene development or population ...θ. The parameter θ represents ... See full document

... and nonlinear terms than the NLSE. It is different to the one for the propagation of TE polarized subwavelength beams ...[6]. We also numerically study the propagation of ... See full document

... paper, we focus on the Calder´ on problem for the fractional semilinear Schr¨ odinger equation, that is, to recover the coefficient q(x, u) from the collected external data set C ... See full document

... To study the interesting properties of parabolic quantum dot, we use parabolic coordinate ...First we transform the coordinate system from spher- ical coordinates (r, θ , ... See full document

... out the blow-up rate and blow-up constant of u (n) of the equation ...result, we have the following results: Theorem 4. If u is the solution of the problem ...of ... See full document

... paper, we study the multiplicity of nontrivial nonnegative solutions for a semilinear elliptic equation involving nonlinear boundary con- dition and sign-changing ...With the ... See full document

... Abstract. We study the blow-up behaviors of solutions of a semilinear heat equation with a nonlinear boundary ...conditions, we prove that the blow-up point occurs only at ... See full document

... 0, the singular limits including semiclassical, nonrelativistic and nonrelativistic- semiclassical limits of the Cauchy problem for the modulated defocusing nonlinear Klein–Gordon ... See full document

... article we study properties of positive solutions of the or- dinary differential equation t 2 u 00 = u n for 1 < n ∈ N, we obtain conditions for their blow-up in finite time, and some ... See full document

... Here the variable t is the independent similarity variable and the function f is related to the stream ...For the detailed derivation, we refer the readers to [9], [5], ... See full document

... §2, we shall first prove that quenching always occurs and then give some preliminary results related to the initial value problem ...Then we prove in §3 the existence of self-similar solutions ... See full document

... 6.8. We would like to point out the striking similarity between the solution w a to the Lam´ e equation and the defining power series of complex elliptic genera in the ... See full document

... From the local existence and uniqueness theorem of ordinary differential equations it follows that there is a unique positive local solution ϕ of (P ) for each given η > 0.. We shall [r] ... See full document

... Using Cayley-Hamilton Theorem to evaluate A.[r] ... See full document

... for the solution of the nonlinear matrix equation X + A T X −1 A = Q (with Q > ...0). The SDA was proven to be convergent quadratically to the maximal solution X + when all ... See full document

... The study is an attempt to offer an account of form-meaning correlations in Taiwanese ...establish the basis for the analysis, we first review in detail the conditional ... See full document

... on the Chinese summary writing task and the pretest/posttest summary writing tasks did not show any significance at ...support the finding that the subjects’ Chinese summative abilities had no ... See full document