Blow-Up Phenomena for a Class of Parabolic or Pseudo-parabolic Equation with Nonlocal Source
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DOI: 10.1007/s00009-021-01735-3
Abstract: In this paper, we consider a class of parabolic or pseudo-parabolic equation with nonlocal source term: $$\begin{aligned} u_t-\nu \triangle u_t-\hbox {div}(\rho (|\nabla u|)^2\nabla u)=u^p(x,t)\int _{\Omega }k(x,y)u^{p+1}(y,t)dy, \end{aligned}$$ where $$\nu \ge 0$$ and $$p>0$$ . Using… read more here.
Keywords: pseudo parabolic; equation nonlocal; class parabolic; parabolic equation ... See more keywords
The critical exponent for fast diffusion equation with nonlocal source
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DOI: 10.1186/s13661-019-1282-1
Abstract: This paper considers the Cauchy problem for fast diffusion equation with nonlocal source ut=Δum+(∫Rnuq(x,t)dx)p−1qur+1$u_{t}=\Delta u^{m}+ (\int_{\mathbb{R}^{n}}u^{q}(x,t)\,dx )^{\frac{p-1}{q}}u^{r+1}$, which was raised in [Galaktionov et al. in Nonlinear Anal. 34:1005–1027, 1998]. We give the critical Fujita exponent… read more here.
Keywords: diffusion equation; nonlocal source; fast diffusion; equation nonlocal ... See more keywords