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
Hopf bifurcation in a reaction-diffusion-advection equation with nonlocal delay effect
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DOI: 10.1016/j.jde.2020.08.026
Abstract: Abstract This paper investigates the dynamics of a general reaction-diffusion-advection equation with nonlocal delay effect and Dirichlet boundary condition. The existence and stability of positive spatially nonhomogeneous steady state solution are shown. By analyzing the… read more here.
Keywords: hopf bifurcation; equation nonlocal; nonlocal delay; 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
Mild solution of stochastic partial differential equation with nonlocal conditions and noncompact semigroups
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DOI: 10.1515/ms-2017-0207
Abstract: Abstract The aim of this paper is to discuss the existence of mild solutions for a class of semilinear stochastic partial differential equation with nonlocal initial conditions and noncompact semigroups in a real separable Hilbert… read more here.
Keywords: noncompact semigroups; differential equation; equation nonlocal; partial differential ... See more keywords
Positive solution for nonlinear fractional differential equation with nonlocal multi-point condition
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DOI: 10.24193/fpt-ro.2020.2.30
Abstract: In this paper, we study and consider the positive solution of fractional differential equation with nonlocal multi-point conditions of the from: RLD q 0+ u(t) + g(t)f(t, u(t)) = 0, t ∈ (0, 1) u(0)… read more here.
Keywords: differential equation; equation nonlocal; positive solution; point ... See more keywords
Family of Asymptotic Solutions to the Two-Dimensional Kinetic Equation with a Nonlocal Cubic Nonlinearity
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DOI: 10.3390/sym14030577
Abstract: We apply the original semiclassical approach to the kinetic ionization equation with the nonlocal cubic nonlinearity in order to construct the family of its asymptotic solutions. The approach proposed relies on an auxiliary dynamical system… read more here.
Keywords: equation; equation nonlocal; family asymptotic; kinetic equation ... See more keywords