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- W4377233038 abstract "The purpose of this work is to analyze the well-posedness and the blow-up of solutions of the higher-order parabolic semilinear equation: $$begin{aligned} u_t+(-varDelta )^{d}u=|x|^{alpha }|u|^{p}+zeta (t){textbf{w}}(x) quad text{ for } (x,t)in mathbb {R}^{N}times (0,infty ), end{aligned}$$ where $$din (0,1)cup mathbb {N}$$ , $$p>1$$ , $$-alpha in (0,min (2d,N))$$ or $$alpha geqslant 0$$ and $$zeta $$ as well as $${textbf{w}}$$ are suitable given functions. The novelty here regard to previous works lies in considering a forcing term $$zeta (t){textbf{w}}(x)$$ depending on both time and space variables, a fractional or high-order Laplace operator $$(-varDelta )^{d}$$ , and a weighted (possibly singular) nonlinearity $$|x|^{alpha }|u|^{p}$$ . We prove small Lebesgue data global existence for p larger than a critical value depending on the behavior of $$zeta $$ . Furthermore, the global existence fails to hold for p less than the critical value under the additional condition $$int _{mathbb {R}^N}{} {textbf {w}}(x),textrm{d}x>0$$ . As a consequence, we derive the explicit value of the Fujita exponent $$p_textrm{F}(sigma )$$ in the case $$zeta (t)=t^sigma ,, sigma >-1$$ ." @default.
- W4377233038 created "2023-05-23" @default.
- W4377233038 creator A5084044092 @default.
- W4377233038 date "2023-05-22" @default.
- W4377233038 modified "2023-09-28" @default.
- W4377233038 title "On the Fujita Exponent for a Hardy–Hénon Equation with a Spatial–Temporal Forcing Term" @default.
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- W4377233038 doi "https://doi.org/10.1007/s44007-023-00049-y" @default.
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