In this paper, an improved method of studying superconvergence and extrapola-tion is presented, whose key point is to obtain superconvergence and extrapolationof u - uh at locally symmetric points by investigating sup...In this paper, an improved method of studying superconvergence and extrapola-tion is presented, whose key point is to obtain superconvergence and extrapolationof u - uh at locally symmetric points by investigating superconvergence and ex-trapolation of uI - uh at locally symmetric points. Using this method, for 2-ordertriangular element, following estimation is discovered:where u*=4uh-u2h/3 0＜e＜1, X is a local symmetric point of Ω, and for p-orderrectiangular element, there exists:|(u - uh)(X)| ≤ chp+3| ln |ln |ln h|||||u||p+4,owhere X is a vertex of local symmetry and p = 2k(k ∈ N, k ≥ 2).展开更多
This paper mainly focuses on the front-like entire solution of a classical nonlocal dispersal equation with ignition nonlinearity. Especially, the dispersal kernel function J may not be symmetric here. The asymmetry o...This paper mainly focuses on the front-like entire solution of a classical nonlocal dispersal equation with ignition nonlinearity. Especially, the dispersal kernel function J may not be symmetric here. The asymmetry of J has a great influence on the profile of the traveling waves and the sign of the wave speeds, which further makes the properties of the entire solution more diverse. We first investigate the asymptotic behavior of the traveling wave solutions since it plays an essential role in obtaining the front-like entire solution. Due to the impact of f′(0) = 0, we can no longer use the common method which mainly depends on Ikehara theorem and bilateral Laplace transform to study the asymptotic rates of the nondecreasing traveling wave and the nonincreasing one tending to 0, respectively, so we adopt another method to investigate them. Afterwards, we establish a new entire solution and obtain its qualitative properties by constructing proper supersolution and subsolution and by classifying the sign and size of the wave speeds.展开更多
文摘In this paper, an improved method of studying superconvergence and extrapola-tion is presented, whose key point is to obtain superconvergence and extrapolationof u - uh at locally symmetric points by investigating superconvergence and ex-trapolation of uI - uh at locally symmetric points. Using this method, for 2-ordertriangular element, following estimation is discovered:where u*=4uh-u2h/3 0＜e＜1, X is a local symmetric point of Ω, and for p-orderrectiangular element, there exists:|(u - uh)(X)| ≤ chp+3| ln |ln |ln h|||||u||p+4,owhere X is a vertex of local symmetry and p = 2k(k ∈ N, k ≥ 2).
基金supported by National Natural Science Foundation of China(Grant Nos.11671180 and 11371179)the Fundamental Research Funds for the Central Universities(Grant No.lzujbky2016-ct12)
文摘This paper mainly focuses on the front-like entire solution of a classical nonlocal dispersal equation with ignition nonlinearity. Especially, the dispersal kernel function J may not be symmetric here. The asymmetry of J has a great influence on the profile of the traveling waves and the sign of the wave speeds, which further makes the properties of the entire solution more diverse. We first investigate the asymptotic behavior of the traveling wave solutions since it plays an essential role in obtaining the front-like entire solution. Due to the impact of f′(0) = 0, we can no longer use the common method which mainly depends on Ikehara theorem and bilateral Laplace transform to study the asymptotic rates of the nondecreasing traveling wave and the nonincreasing one tending to 0, respectively, so we adopt another method to investigate them. Afterwards, we establish a new entire solution and obtain its qualitative properties by constructing proper supersolution and subsolution and by classifying the sign and size of the wave speeds.
