A nonlinear parabolic problem with singular terms and nonregular data [PDF]
, 2019 We study existence of nonnegative solutions to a nonlinear parabolic boundary value problem with a general singular lower order term and a nonnegative measure as nonhomogeneous datum, of the form $$ \begin{cases} \dys u_t - \Delta_p u = h(u)f ...
Oliva, Francescantonio +1 more
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Almost classical solutions to the total variation flow [PDF]
, 2011 The paper examines one-dimensional total variation flow equation with Dirichlet boundary conditions. Thanks to a new concept of "almost classical" solutions we are able to determine evolution of facets -- flat regions of solutions.
Kielak, Karolina +2 more
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Periodic total variation flow of non-divergence type in Rn [PDF]
, 2013 We introduce a new notion of viscosity solutions for a class of very singular nonlinear parabolic problems of non-divergence form in a periodic domain of arbitrary dimension, whose diffusion on flat parts with zero slope is so strong that it becomes a ...
Giga, Mi-Ho +2 more
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Self-Similar Blow-Up Profiles for a Reaction-Diffusion Equation with Strong Weighted Reaction
Advanced Nonlinear Studies, 2020 We study the self-similar blow-up profiles associated to the following second-order reaction-diffusion equation with strong weighted reaction and unbounded weight:
Iagar Razvan Gabriel, Sánchez Ariel
doaj +1 more source
Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction [PDF]
, 2011 We study a singular-limit problem arising in the modelling of chemical reactions. At finite {\epsilon} > 0, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential.
A. Blanchet +35 more
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Carleman estimates and null controllability of a class of singular parabolic equations
Advances in Nonlinear Analysis, 2018 In this paper, we consider control systems governed by a class of semilinear parabolic equations, which are singular at the boundary and possess singular convection and reaction terms.
Du Runmei +3 more
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On the viscous Cahn-Hilliard equation with singular potential and inertial term
, 2016 We consider a relaxation of the viscous Cahn-Hilliard equation induced by the second-order inertial term~$u_{tt}$. The equation also contains a semilinear term $f(u)$ of "singular" type. Namely, the function $f$ is defined only on a bounded interval of ${
Scala, Riccardo, Schimperna, Giulio
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A Boundary Estimate for Singular Parabolic Diffusion Equations
, 2017 We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of p-laplacian type.
Gianazza, Ugo +2 more
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Large time behavior for the fast diffusion equation with critical absorption [PDF]
, 2016 International audienceWe study the large time behavior of nonnegative solutions to the Cauchy problem for a fast diffusion equation with critical zero order absorption$$\partial_{t}u-\Delta u^m+u^q=0 \quad \quad \hbox{in} \(0,\infty)\times\real^N ...
Benachour, Said +2 more
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Weak formulation for singular diffusion equation with dynamic boundary condition
, 2017 In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a governing ...
A. Ito +19 more
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