Author
Yuanwei Qi
Other affiliations: Hong Kong University of Science and Technology, University of Minnesota, University of California ...read more
Bio: Yuanwei Qi is an academic researcher from University of Central Florida. The author has contributed to research in topics: Initial value problem & Cauchy problem. The author has an hindex of 15, co-authored 57 publications receiving 698 citations. Previous affiliations of Yuanwei Qi include Hong Kong University of Science and Technology & University of Minnesota.
Papers published on a yearly basis
Papers
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TL;DR: In this paper, the authors studied the Cauchy problem in Rn of general parabolic equations which take the form ut = Δum + ts|x|σup with non-negative initial value.
Abstract: In this paper we study the Cauchy problem in Rn of general parabolic equations which take the form ut = Δum + ts|x|σup with non-negative initial value. Here s ≧ 0, m > (n − 2)+/n, p > max (1, m) and σ > − 1 if n = 1 or σ > − 2 if n ≧ 2. We prove, among other things, that for p ≦ pc, where pc ≡ m + s(m − 1) + (2 + 2s + σ)/n > 1, every nontrivial solution blows up in finite time. But for p > pc a positive global solution exists.
102 citations
TL;DR: On etudie l'existence de la solution non constante bornee de l'equation differentielle ΔW-y ⊇W/2+/W/P−1 -W -W/(p-1)=0 dans R n, n2 avec pp c ou P c =(n+2)/(n-2) est l'exposant de l'sespace de Sobolev critique for R n.
55 citations
TL;DR: In this paper, the Cauchy problem is studied and the fastest decaying in time of solutions with the fastest decay in time is constructed, where positive global solutions and non-global solutions are obtained.
Abstract: The Cauchy problemut=Δuα +vp,vt=Δvβ +uq is studied, wherex eRN, 0 1 + 2 max(p + β, q + α)/n then there exist both positive global solutions and non-global solutions. In addition, the decaying in time of solutions tout,=Δuα inRn × (0, ∞), an equation which occurs naturally in our study of above systems, is studied and solutions with the fastest decaying in time are constructed.
49 citations
TL;DR: It is shown rigorously that there exists a $v_{\min}$ such that there is a travelling wave of speed v if and only $v \geq v_{\ min}$.
Abstract: This article studies propagating wave fronts in an isothermal chemical reaction $ A + 2B \rightarrow 3B$ involving two chemical species, a reactant A and an autocatalyst B, whose diffusion coefficients, $D_A$ and $D_B$, are unequal due to different molecular weights and/or sizes. Explicit bounds $v_*$ and $v^*$ that depend on $D_B/D_A$ are derived such that there is a unique travelling wave of every speed $v \geq v^*$ and there does not exist any travelling wave of speed $v
42 citations
TL;DR: In this article, a strongly coupled partial differential equation model with a non-monotonic functional response was considered and the existence and non-existence results concerning non-constant steady states (patterns) of the underlying system were proved.
Abstract: The predator–prey system with non-monotonic functional response is an interesting field of theoretical study In this paper we consider a strongly coupled partial differential equation model with a non-monotonic functional response—a Holling type-IV function in a bounded domain with no flux boundary condition We prove a number of existence and non-existence results concerning non-constant steady states (patterns) of the underlying system In particular, we demonstrate that cross-diffusion can create patterns when the corresponding model without cross-diffusion fails
41 citations
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Book•
04 Oct 2007
TL;DR: In this article, the authors propose a model for solving the model elliptic problems and model parabolic problems. But their model is based on Equations with Gradient Terms (EGS).
Abstract: Preliminaries.- Model Elliptic Problems.- Model Parabolic Problems.- Systems.- Equations with Gradient Terms.- Nonlocal Problems.
935 citations
TL;DR: In this article various extensions of an old result of Fujita are considered for the initial value problem for the reaction-diffusion equation u_t =Delta u + u^p in $R^N with nonnegative initial values.
Abstract: In this article various extensions of an old result of Fujita are considered for the initial value problem for the reaction-diffusion equation $u_t = \Delta u + u^p $ in $R^N $ with $p > 1$ and nonnegative initial values. Fujita showed that if $1 1 + {2 / N}$, there were nontrivial global solutions. This paper discusses similar results for other geometries and other equations including a nonlinear wave equation and a nonlinear Schrodinger equation.
754 citations
TL;DR: In this paper, the authors revisited the literature since 1990 and showed that for positive solutions, the initial value problem does not have any nontrivial, non-negative solution existing on R N ǫ×ǫ[0,ǫ∞] (a global solution), whereas if pǫ>ǫ p c, there exist global, small data, positive solutions as well as solutions which are non-global.
516 citations
TL;DR: In this article, the authors constructed new families of Kahler-Ricci solitons on complex line bundles over ℂℙn−1, n ≥ 2, and exhibited a noncompact Ricci flow that shrinks smoothly and self-similarly for t 0.
Abstract: We construct new families of Kahler-Ricci solitons on complex line bundles over ℂℙn−1, n ≥ 2. Among these are examples whose initial or final condition is equal to a metric cone ℂn/ℤk. We exhibit a noncompact Ricci flow that shrinks smoothly and self-similarly for t 0; this evolution is smooth in space-time except at a single point, at which there is a blowdown of a ℂℙn−1. We also construct certain shrinking solitons with orbifold point singularities.
300 citations