Results 1 to 10 of about 43 (43)
Fractional parabolic problems with a nonlocal initial condition
Moroccan Journal of Pure and Applied Analysis, 2017 In this work we will consider a class of non local parabolic problems with nonlocal initial condition, more precisely we deal with the ...
Abdellaoui B. +2 more
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Lack of smoothing for bounded solutions of a semilinear parabolic equation
Advances in Nonlinear Analysis, 2020 We study a semilinear parabolic equation that possesses global bounded weak solutions whose gradient has a singularity in the interior of the domain for all t > 0.
Fila Marek, Lankeit Johannes
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Advances in Nonlinear Analysis, 2014 We obtain a new Liouville comparison principle for weak solutions (u,v) of semilinear parabolic second-order partial differential inequalities of the form ut-ℒu-|u|q-1u≥vt-ℒv-|v|q-1v(*)$u_t -{\mathcal {L}}u- |u|^{q-1}u\ge v_t -{\mathcal {L}}v- |v|^{q-1}v\
Kurta Vasilii V.
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Hypercontractivity, supercontractivity, ultraboundedness and stability in semilinear problems
Advances in Nonlinear Analysis, 2017 We study the Cauchy problem associated to a family of nonautonomous semilinear equations in the space of bounded and continuous functions over ℝd{\mathbb{R}^{d}} and in Lp{L^{p}}-spaces with respect to tight evolution systems of measures.
Addona Davide +2 more
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Advances in Nonlinear Analysis, 2018 We investigate the asymptotic behavior of solutions to a semilinear heat equation with homogeneous Neumann boundary conditions. It was recently shown that the nontrivial kernel of the linear part leads to the coexistence of fast solutions decaying to 0 ...
Ghisi Marina +2 more
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Advanced Nonlinear StudiesIn this paper, we consider the general dual fractional parabolic problem ∂tαu(x,t)+Lu(x,t)=f(t,u(x,t))inRn×R. ${\partial }_{t}^{\alpha }u\left(x,t\right)+\mathcal{L}u\left(x,t\right)=f\left(t,u\left(x,t\right)\right) \text{in} {\mathbb{R}}^{n}{\times ...
Guo Yahong, Ma Lingwei, Zhang Zhenqiu
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Continuous in time bubble decomposition for the harmonic map heat flow
Forum of Mathematics, PiWe consider the harmonic map heat flow for maps $\mathbb {R}^{2} \to \mathbb {S}^2$ . It is known that solutions to the initial value problem exhibit bubbling along a well-chosen sequence of times.
Jacek Jendrej +2 more
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Global existence and finite-time blowup for a mixed pseudo-parabolic r(x)-Laplacian equation
Advances in Nonlinear AnalysisThis article is devoted to the study of the initial boundary value problem for a mixed pseudo-parabolic r(x)r\left(x)-Laplacian-type equation. First, by employing the imbedding theorems, the theory of potential wells, and the Galerkin method, we ...
Cheng Jiazhuo, Wang Qiru
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Monotonicity of solutions for parabolic equations involving nonlocal Monge-Ampère operator
Advances in Nonlinear AnalysisIn this article, we consider the parabolic equations with nonlocal Monge-Ampère operators ∂u∂t(x,t)−Dsθu(x,t)=f(u(x,t)),(x,t)∈R+n×R.\frac{\partial u}{\partial t}\left(x,t)-{D}_{s}^{\theta }u\left(x,t)=f\left(u\left(x,t)),\hspace{1.0em}\left(x,t)\in ...
Du Guangwei, Wang Xinjing
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A Liouville theorem for superlinear parabolic equations on the Heisenberg group
Advanced Nonlinear StudiesWe consider a parabolic nonlinear equation on the Heisenberg group. Applying the Gidas–Spruck type estimates, we prove that under suitable conditions, the equation does not have positive solutions. As an application of the nonexistence result, we provide
Wei Juncheng, Wu Ke
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