Existence and non-existence of global solutions for a heat equation with degenerate coefficients
نویسندگان
چکیده
In this paper, the parabolic problem $$u_t - div(\omega (x) \nabla u)= h(t) f(u) + l(t) g(u)$$ with non-negative initial conditions pertaining to $$C_b({\mathbb {R}}^N)$$ , will be studied, where weight $$\omega $$ is an appropriate function that belongs Muckenhoupt class $$A_{1 \frac{2}{N}}$$ and functions f, g, h l are continuous. The main goal establish global non-global existence of solutions. addition, obtained both so-called Fujita’s exponent second critical in sense Lee Ni (Trans Am Math Soc 333(1):365–378, 1992), particular case when $$h(t)\sim t^r \,(r>-1)$$ $$l(t)\sim t^s \, (s>-1)$$ $$f(u)=u^p$$ $$g(u)=(1+u)[\ln (1+u)]^p$$ . results paper extend those by Fujishima et al. (Calc Var Partial Differ Equ 58:62, 2019) worked $$h(t)=1$$ $$l(t)=0$$ $$f(u)=u^p
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ژورنال
عنوان ژورنال: Partial Differential Equations And Applications
سال: 2022
ISSN: ['2662-2971', '2662-2963']
DOI: https://doi.org/10.1007/s42985-022-00210-2