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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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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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
core +2 more sources
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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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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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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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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Optimal waiting time bounds for some flux-saturated diffusion equations
, 2017 We consider the Cauchy problem for two prototypes of flux-saturated diffusion equations. In arbitrary space dimension, we give an optimal condition on the growth of the initial datum which discriminates between occurrence or nonoccurrence of a waiting ...
Giacomelli, Lorenzo +2 more
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Existence of solutions for degenerate parabolic equations with singular terms
, 2015 In this paper we deal with parabolic problems whose simplest model is $$ \begin{cases} u'- \Delta_{p} u + B\frac{|\nabla u|^p}{u} = 0 & \text{in} (0,T) \times \Omega,\newline u(0,x)= u_0 (x) &\text{in}\ \Omega, \newline u(t,x)=0 &\text{on}\ (0,T ...
Dall'Aglio, Andrea +2 more
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Anisotropic total variation flow of non-divergence type on a higher dimensional torus [PDF]
, 2013 We extend the theory of viscosity solutions to a class of very singular nonlinear parabolic problems of non-divergence form in a periodic domain of an arbitrary dimension with diffusion given by an anisotropic total variation energy. We give a proof of a
Giga, Mi-Ho +2 more
core +2 more sources