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531.
532.
This paper considers a fast diffusion equation with potential ut= um V (x)um+upin Rn×(0,T), where 1 2αm+n< m ≤ 1, p > 1, n ≥ 2, V (x) ~ω|x|2with ω≥ 0 as |x| →∞,and α is the positive root of αm(αm + n 2) ω = 0. The critical Fujita exponent was determined as pc= m +2αm+nin a previous paper of the authors. In the present paper,we establish the second critical exponent to identify the global and non-global solutions in their co-existence parameter region p > pcvia the critical decay rates of the initial data.With u0(x) ~ |x| aas |x| →∞, it is shown that the second critical exponent a =2p m,independent of the potential parameter ω, is quite different from the situation for the critical exponent pc. 相似文献
533.
Yamin Wang 《Mathematische Nachrichten》2023,296(5):2150-2166
Let be a closed Riemann surface. Let ψ, h be two smooth functions on Σ with and . In this paper, using the method of flow due to Castras (Pacific J. Math. 276(2015), no. 2, 321–345) and Sun–Zhu (Calc. Var. Partial Differential Equations 60(2021), no. 1, 26), we prove that the solution of the equation exists under given conditions. This gives a new proof of the main results of Zhu (Nonlinear Anal. 169(2018), 38–58). 相似文献
534.
535.
Alessandro Columbu Silvia Frassu Giuseppe Viglialoro 《Studies in Applied Mathematics》2023,151(4):1349-1379
This paper deals with unbounded solutions to a class of chemotaxis systems. In particular, for a rather general attraction–repulsion model, with nonlinear productions, diffusion, sensitivities, and logistic term, we detect Lebesgue spaces where given unbounded solutions also blow up in the corresponding norms of those spaces; subsequently, estimates for the blow-up time are established. Finally, for a simplified version of the model, some blow-up criteria are proved. More precisely, we analyze a zero-flux chemotaxis system essentially described as (⋄) The problem is formulated in a bounded and smooth domain Ω of , with , for some , , , and with . A sufficiently regular initial data is also fixed. Under specific relations involving the above parameters, one of these always requiring some largeness conditions on ,
- (i) we prove that any given solution to (), blowing up at some finite time becomes also unbounded in -norm, for all ;
- (ii) we give lower bounds T (depending on ) of for the aforementioned solutions in some -norm, being ;
- (iii) whenever , we establish sufficient conditions on the parameters ensuring that for some u0 solutions to () effectively are unbounded at some finite time.
536.
本文巧妙应用广义Sobolev不等式,研究了一类拟线性抛物型方程解的爆破时间的下界,该结果推广了文献[1]中的定理2.1和定理3.1的结论,同样完善了文献[2]中的模型(4.1)的结论. 相似文献
537.
538.
A parabolic–elliptic Keller–Segel system with homogeneous Neumann boundary condition is considered in a radially symmetric domain where and is a -dimensional ball of radius We assert that under a condition on the initial data, radial weak solutions blow-up in finite time when 相似文献
539.