Existence of Solutions to the Poisson-Nernst-Planck System with Singular Permanent Charges in $\mathbb{R}^2$ [PDF]
SIAM Journal on Mathematical Analysis, 2021 In this paper, we study the well-posedness of Poisson–Nernst–Planck system with no-flux boundary condition and singular permanent charges in two dimension. The main difficulty comes from the lack of integrability of singular permanent charges.
C. Hsieh, Yongjiang Yu
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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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On the role of kinetic and interfacial anisotropy in the crystal growth theory
, 2012 A planar anisotropic curvature flow equation with constant driving force term is considered when the interfacial energy is crystalline. The driving force term is given so that a closed convex set grows if it is sufficiently large.
M. Giga, Y. Giga
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Flux-saturated porous media equations and applications
, 2015 The aim of this paper is to review the main recent results about the dynamics of nonlinear partial differential equations describing flux-saturated transport mechanisms, eventually in combination with porous media flow and/or reactions terms.
J. Calvo +4 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
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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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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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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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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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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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