Existence of mild solutions for a singular parabolic equation and stabilization
Advances in Nonlinear Analysis, 2015 In this paper, we study the existence and the uniqueness of a positive mild solution for the following singular nonlinear problem with homogeneous Dirichlet boundary conditions: (St) ∂tu - Δpu = u -δ + f(x,u) in (0,T) × Ω =: QT, u = 0 on (0,T) × ∂Ω, u ...
Bougherara Brahim, Giacomoni Jacques
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Regularity of solutions of the parabolic normalized p-Laplace equation
Advances in Nonlinear Analysis, 2018 The parabolic normalized p-Laplace equation is studied. We prove that a viscosity solution has a time derivative in the sense of Sobolev belonging locally to L2{L^{2}}.
Høeg Fredrik Arbo, Lindqvist Peter
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A natural approach to the asymptotic mean value property for the $p$-Laplacian [PDF]
, 2016 Let $1\le p\le\infty$. We show that a function $u\in C(\mathbb R^N)$ is a viscosity solution to the normalized $p$-Laplace equation $\Delta_p^n u(x)=0$ if and only if the asymptotic formula $$ u(x)=\mu_p(\ve,u)(x)+o(\ve^2) $$ holds as $\ve\to 0$ in the ...
Ishiwata, Michinori +2 more
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A Picone identity for variable exponent operators and applications
Advances in Nonlinear Analysis, 2019 In this work, we establish a new Picone identity for anisotropic quasilinear operators, such as the p(x)-Laplacian defined as div(|∇ u|p(x)−2 ∇ u).
Arora Rakesh +2 more
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CLASSIFICATION OF EXTINCTION PROFILES FOR A ONE-DIMENSIONAL DIFFUSIVE HAMILTON-JACOBI EQUATION WITH CRITICAL ABSORPTION [PDF]
, 2018 International audienceA classification of the behavior of the solutions f (·, a) to the ordinary differential equation (|f ′ |^{p−2} f ′) ′ + f − |f ′ |^{p−1} = 0 in (0, ∞) with initial condition f (0, a) = a and f ′ (0, a) = 0 is provided, according to ...
Iagar, Razvan,, Laurençot, Philippe
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Extinction for a Singular Diffusion Equation with Strong Gradient Absorption Revisited
Advanced Nonlinear Studies, 2018 When 2N/(N+1)
Iagar Razvan Gabriel +1 more
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Existence of weak solutions for a PDE system describing phase separation and damage processes including inertial effects [PDF]
, 2014 In this paper, we consider a coupled PDE system describing phase separation and damage phenomena in elastically stressed alloys in the presence of inertial effects.
Heinemann, Christian, Kraus, Christiane
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Hölder gradient estimates for a class of singular or degenerate parabolic equations
Advances in Nonlinear Analysis, 2017 We prove interior Hölder estimates for the spatial gradients of the viscosity solutions to the singular or degenerate parabolic ...
Imbert Cyril +2 more
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Evolutionary quasi-variational and variational inequalities with constraints on the derivatives
Advances in Nonlinear Analysis, 2018 This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination of partial ...
Miranda Fernando +2 more
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Ireneo Peral: Forty Years as Mentor
Advanced Nonlinear Studies, 2017 In this article we present a survey of the Ph.D. theses that have been completed under the advice of Ireneo Peral.Following a chronological order, we summarize the main results contained in the works of the former students of Ireneo Peral.
Abdellaoui Boumediene +9 more
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