The blow-up solutions for fractional heat equations on torus and Euclidean space

被引：0
|
作者：
Bhimani, Divyang G. [1 ]
机构：
[1] Indian Inst Sci Educ & Res, Dept Math, Dr Homi Bhabha Rd, Pune 411008, India
来源：
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2023年 / 30卷 / 02期
关键词：
Fractional heat equations; Blow-up solution; Modulation spaces; Fourier amalgam spaces; MODULATION SPACES; CAUCHY-PROBLEM;
D O I：
10.1007/s00030-022-00828-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We produce a finite time blow-up solution for nonlinear fractional heat equation (partial derivative(t)u + (-Delta)(beta /2) u= u(k)) in modulation and Fourier amalgam spaces on the torus T-d and the Euclidean space R-d. This complements several known local and small data global well-posedness results in modulation spaces on R-d. Our method of proof rely on the formal solution of the equation. This method should be further applied to other non-linear evolution equations.
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页数：22
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