具有非齐次权重的半线性热传导方程的Fujita指数Fujita exponent of semilinear heat equation with nonhomogeneous weights
黄思雨,李红洁,杨晗
摘要(Abstract)：
主要研究了具有非齐次权重的半线性热传导方程的Fujita指数。当问题中的权重函数■时，得到Fujita指数■;当非线性项指数p>p_c时，运用压缩映像原理，得到在加权Lorentz空间小初值条件下整体解的存在性；当非线性项指数1
关键词(KeyWords)：
Fujita指数;整体解;爆破;加权Lorentz空间
基金项目(Foundation):
国家自然科学基金资助项目(12371178,11971394)
作者(Author):
黄思雨,李红洁,杨晗
DOI:
10.13482/j.issn1001-7011.2026.04.218
参考文献(References)：
- [1] FUJITA H.On the blowing up of solutions of the Cauchy problem for ut=Δu+u1+α [J].Journal of the Faculty of Science University of Tokyo,1966,13:109-124.
- [2] HAYAKAWA K.On nonexistence of global solutions of some semilinear parabolic differential equations [J].Proceedings of the Japan Academy,1973,49(7):503-505.
- [3] KOBAYASHI K,SIRAO T,TANAKA H.On the growing up problem for semilinear heat equations [J].Journal of the Mathematical Society of Japan,1977,29(3):407-424.
- [4] WEISSLER F B.Existence and non-existence of global solutions for a semilinear heat equation [J].Israel Journal of Mathematics,1981,38(1):29-40.
- [5] FERREIRA R,DE PABLO A,P??REZ-LLANOS M,et al.Critical exponents for a semilinear parabolic equation with variable reaction [J].Proceedings of the Royal Society of Edinburgh Section A:Mathematics,2012,142(5):1027-1042.
- [6] GHOUL T E,NGUYEN V T,ZAAG H.Construction of type I blowup solutions for a higher order semilinear parabolic equation [J].Advances in Nonlinear Analysis,2019,9(1):388-412.
- [7] GUO W,WANG X,ZHOU M.Asymptotic behavior of solutions to a class of semilinear parabolic equations [J].Boundary Value Problems,2016,2016(1):1-9.
- [8] LIAN W,WANG J,XU R.Global existence and blow up of solutions for pseudo-parabolic equation with singular potential [J].Journal of Differential Equations,2020,269(6):4914-4959.
- [9] CASTILLO R,GUZMAN-REA O,ZEGARRA M.Existence and non-existence of global solutions for a heat equation with degenerate coefficients [J].Partial Differential Equations and Applications,2022,3(6):1-16.
- [10] ZHOU Y,LENG Y,NIE Y.Fujita type theorem for a class of coupled quasilinear convection-diffusion equations [J].Boundary Value Problems,2021,2021(1):1-20.
- [11] SUGITANI S.On nonexistence of global solutions for some nonlinear integral equations [J].Osaka Journal of Mathematics,1975,12(1):45-51.
- [12] GALAKTIONOV V A.Blow-up for quasilinear heat equations with critical Fujita’s exponents [J].Proceedings of the Royal Society of Edinburgh Section A:Mathematics,1994,124(3):517-525.
- [13] GALAKTIONOV V A.Unbounded solutions of the Cauchy problem for the parabolic equation ut=??(uσ??u)+uβ [J].Soviet Physics Doklady.1980,25:458-459.
- [14] PINSKY R G.Existence and nonexistence of global solutions for ut=Δu+a(x)up in Rd[J].Journal of Differential Equations,1997,133(1):152-177.
- [15] FUJISHIMA Y,KAWAKAMI T,SIRE Y.Critical exponent for the global existence of solutions to a semilinear heat equation with degenerate coefficients [J].Calculus of Variations and Partial Differential Equations,2019,58(2):62.
- [16] KAWAKAMI,SIRE Y,WANG J N.Fujita exponent for the global-in-time solutions to a semilinear heat equation with non-homogeneous weights [J].Journal of Evolution Equations,2024,24(2):44.
- [17] GRAFAKOS L.Classical Fourier analysis [M].New York:Springer,2008.
- [18] BAUDOIN F.Geometric inequalities on Riemannian and sub-Riemannian manifolds by heat semigroups techniques [M].New Trends on Analysis and Geometry in Metric Spaces:Levico Terme,Italy 2017.Cham:Springer International Publishing,2021.
- [19] MUCKENHOUPT B.Weighted norm inequalities for the Hardy maximal function [J].Transactions of the American Mathematical Society,1972,165:207-226.
- [20] ALESSA R,ALSHEHRI A,ALTAMIMI H,et al.Local well-posedness and blow-up for an inhomogeneous nonlinear heat equation [J].Mathematical Methods in the Applied Sciences,2020,43(8):5264-5272.