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Asymptotic behavior for nonlocal diffusion equations
We study the asymptotic behavior for nonlocal diffusion models of the form ut=J∗u−u in the whole RN or in a bounded smooth domain with Dirichlet or Neumann boundary conditions. In RN we obtain thatExpand
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Regional blow-up for a higher-order semilinear parabolic equation
We study the blow-up behaviour of solutions of a 2mth order semilinear parabolic equation [formula here] with a superlinear function q(u) for |u| Gt; 1. We prove some estimates on the asymptoticExpand
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Regularity results for the blow-up time as a function of the initial data
We study the dependence of the finite blow-up time with respect to the initial data for solutions of the equation ut = ∆u + u. We obtain Lipschitz continuity for a certain class of initial data andExpand
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On Uniqueness of Positive Solutions of Semilinear Elliptic Equations with Singular Potential
Abstract We prove the uniqueness of positive W01,2 solutions for the following problem, which involves the singular potential |x|-2 : where N ≥ 3, 1 < p < , and 0 < λ < . We also give a completeExpand
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L∞ and decay estimates for higher-order semilinear diffusion–absorption equations
Abstract We derive estimates of solutions of the semilinear 2mth-order parabolic equation of diffusion–absorption type u t = − ( − Δ ) m u − | u | p − 1 u in R N × R + , m ⩾ 2 , p > 1 , with boundedExpand
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On source-type solutions and the Cauchy problem for a doubly degenerate sixth-order thin film equation, I: Local oscillatory properties
Abstract As a key example, the sixth-order doubly degenerate parabolic equation from thin film theory, u t = ( | u | m | u x x x x x | n u x x x x x ) x in R × R + , with two parameters, n ≥ 0 and mExpand
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On uniqueness for ODEs Arising in Blow-up Asymptotics for Nonlinear Heat Equations
Abstract We study uniqueness for nonlinear ordinary differential equations arising in constructing blow-up and extinction self-similar solutions of various reaction-diffusion- absorption equations.Expand
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On Uniqueness and Stability of Self-Similar Blow-Up Solutions of Nonlinear Heat Equations: Evolution Approach
We present evolution arguments of studying uniqueness and asymptotic stability of blow-up self-similar solutions of second-order nonlinear parabolic equations from combustion and filtration theory.Expand
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