BLOW-UP FOR DISCRETIZATIONS OF SOME REACTION-DIFFUSION EQUATIONS WITH A NONLINEAR CONVECTION TERM
, 2016 This paper concerns the study of the numerical approximation for the following parabolic equations with a nonlinear convection term ut(x, t) = uxx(x, t) − u (x, t)ux(x, t) + u (x, t), 0 < x < 1, t > 0, ux(0, t) = 0, ux(1, t) = 0, t > 0, u(x, 0 ...
D. Nabongo, N. Koffi, T. K. Augustin
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A-priori bounds for quasilinear problems in critical dimension
Advances in Nonlinear Analysis, 2019 We establish uniform a-priori bounds for solutions of the quasilinear ...
Romani Giulio
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Solutions of the Camassa-Holm equation with accumulating breaking times [PDF]
Dynamics of PDE 13, 91-105 (2016), 2015 We present two initial profiles to the Camassa-Holm equation which yield solutions with accumulating breaking times.
arxiv +1 more source
, 2016 In this paper, we consider the following nonlinear elliptic system: (P) ⎧⎨ ⎩ −Δp(x)u = ua(x)vb(x), x ∈ Ω, −Δq(x)v = uc(x)ve(x) , x ∈ Ω, u > 0, v > 0, in a smooth bounded domain Ω ⊂ RN , with different Dirichlet boundary conditions u = λ , v = μ , u = v =
S. Medjbar, S. Tas
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Lane-Emden equations perturbed by nonhomogeneous potential in the super critical case
Advances in Nonlinear Analysis, 2021 Our purpose of this paper is to study positive solutions of Lane-Emden ...
Ma Yong, Wang Ying, Ledesma César T.
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Single point blow-up solutions to the heat equation with nonlinear boundary conditions
, 2013 We study finite blow-up solutions of the heat equation with nonlinear boundary conditions. We provide a sufficient condition for the single point blow-up at the origin and a precise spacial singularity of the blow-up profile.
J. Harada
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Well-Posedness and Uniform Decay Rates for a Nonlinear Damped Schrödinger-Type Equation
Advanced Nonlinear Studies, 2021 In this paper we study the existence as well as uniform decay rates of the energy associated with the nonlinear damped Schrödinger equation,
Cavalcanti Marcelo M. +1 more
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Blowup for the nonlinear Schrödinger equation with an inhomogeneous damping term in the $L^2$ critical case [PDF]
, 2014 We consider the nonlinear Schr\"odinger equation with $L^2$-critical exponent and an inhomogeneous damping term. By using the tools developed by Merle and Raphael, we prove the existence of blowup phenomena in the energy space $H^1(\mathbb{R})$.
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Fast and Slow Decaying Solutions of Lane–Emden Equations Involving Nonhomogeneous Potential
Advanced Nonlinear Studies, 2020 Our purpose in this paper is to study positive solutions of the Lane–Emden ...
Chen Huyuan, Huang Xia, Zhou Feng
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Solution to the semilinear wave equation with a pyramid-shaped blow-up surface
, 2016 We consider the semilinear wave equation with subconformal power nonlinearity in two space dimensions. We construct a finite-time blow-up solution with an isolated characteristic blow-up point at the origin, and a blow-up surface which is centered at the
F. Merle, H. Zaag
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