CLASSIFICATION OF LOCAL ASYMPTOTICS FOR SOLUTIONS TO HEAT EQUATIONS WITH INVERSE-SQUARE POTENTIALS
CLASSIFICATION OF LOCAL ASYMPTOTICS FOR SOLUTIONS TO HEAT EQUATIONS WITH INVERSE-SQUARE POTENTIALS
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DOI：
10.3934/dcds.2011.31.65
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发表时间：
2010-02
影响因子：
1.1
通讯作者：
V. Felli;A. Primo
中科院分区：
文献类型：
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作者：
V. Felli;A. Primo
研究了具有空间奇异平方反比势的热方程解的渐近性态。将抛物型Almgren型单调性公式与Blow-up方法相结合，研究了具有哈代型位势的线性和亚临界半线性抛物方程解在奇异点附近的精确性态.作为一个显着的副产品，一个独特的连续性得到。
Asymptotic behavior of solutions to heat equations with spatially singular inverse-square potentials is studied. By combining a parabolic Almgren type monotonicity formula with blow-up methods, we evaluate the exact behavior near the singularity of solutions to linear and subcritical semilinear parabolic equations with Hardy type potentials. As a remarkable byproduct, a unique continuation property is obtained.