Uniqueness for fractional parabolic and elliptic equations with drift [PDF]
arXiv, 2022 We investigate uniqueness, in suitable weighted Lebesgue spaces, of solutions to a class of fractional parabolic and elliptic equations with a drift.
arxiv
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
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
doaj +1 more source
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
doaj +1 more source
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
core +2 more sources
On a class of fully nonlinear parabolic equations
Advances in Nonlinear Analysis, 2016 We study the homogeneous Dirichlet problem for the fully nonlinear ...
Antontsev Stanislav, Shmarev Sergey
doaj +1 more source
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
core +1 more source
Parabolic Biased Infinity Laplacian Equation Related to the Biased Tug-of-War
Advanced Nonlinear Studies, 2019 In this paper, we study the parabolic inhomogeneous β-biased infinity Laplacian equation arising from the β-biased tug-of ...
Liu Fang, Jiang Feida
doaj +1 more source
On some parabolic problems with measure sources
Moroccan Journal of Pure and Applied Analysis, 2019 One of the recent advances in the investigation of nonlinear parabolic equations with a measure as forcing term is a paper by F. Petitta in which it has been introduced the notion of renormalized solutions to the initial parabolic problem in divergence ...
Abdellaoui Mohammed
doaj +1 more source
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
core +1 more source