A Fredholm Transformation for the Rapid Stabilization of a Degenerate Parabolic Equation [PDF]
SIAM Journal of Control and Optimization, 2020 This paper deals with the rapid stabilization of a degenerate parabolic equation with a right Dirich-let control. Our strategy consists in applying a backstepping strategy, which seeks to find an invertible transformation mapping the degenerate parabolic
L. Gagnon, P. Lissy, S. Marx
semanticscholar +1 more source
Higher regularity for weak solutions to degenerate parabolic problems [PDF]
Calculus of Variations and Partial Differential Equations, 2023 In this paper, we study two related features of the regularity of the weak solutions to the following strongly degenerate parabolic equation $$\begin{aligned} u_t-\textrm{div}\left( \left( \left| Du\right| -1\right) _+^{p-1}\frac{Du}{\left| Du\right ...
Andrea Gentile +1 more
semanticscholar +1 more source
Convergence of Inverse Volatility Problem Based on Degenerate Parabolic Equation
Mathematics, 2022 Based on the theoretical framework of the Black–Scholes model, the convergence of the inverse volatility problem based on the degenerate parabolic equation is studied.
Yilihamujiang Yimamu, Zuicha Deng
doaj +1 more source
The Cauchy Problem for Parabolic Equations with Degeneration [PDF]
Advances in Mathematical Physics, 2020 Annotation. For a second-order parabolic equation, the multipoint in time Cauchy problem is considered. The coefficients of the equation and the boundary condition have power singularities of arbitrary order in time and space variables on a certain set of points.
Ivan Pukal’skii, Bohdan Yashan
openaire +2 more sources
Regularity results for a class of widely degenerate parabolic equations [PDF]
Advances in Calculus of Variations, 2022 Motivated by applications to gas filtration problems, we study the regularity of weak solutions to the strongly degenerate parabolic PDE u t - div ( ( | D u | - ν ) + p - 1 D u | D u | ) = f in Ω T = Ω × ( 0 , T ) , u_{t}-\operatorname{div}\
Pasquale Ambrosio +1 more
semanticscholar +1 more source
Saturated Fronts in Crowds Dynamics
Advanced Nonlinear Studies, 2021 We consider a degenerate scalar parabolic equation, in one spatial dimension, of flux-saturated type. The equation also contains a convective term. We study the existence and regularity of traveling-wave solutions; in particular we show that they can be ...
Campos Juan +2 more
doaj +1 more source
Existence and cost of boundary controls for a degenerate/singular parabolic equation [PDF]
Mathematical Control and Related Fields, 2020 In this paper, we consider the following degenerate/singular parabolic equation $$ u_t -(x^\alpha u_{x})_x - \frac{\mu}{x^{2-\alpha}} u =0, \qquad x\in (0,1), \ t \in (0,T), $$ where $0\leq \alpha
U. Biccari +2 more
semanticscholar +1 more source
An energy formula for fully nonlinear degenerate parabolic equations in one spatial dimension [PDF]
Mathematische Annalen, 2022 Energy (or Lyapunov) functions are used to prove stability of equilibria, or to indicate a gradient-like structure of a dynamical system. Matano constructed a Lyapunov function for quasilinear non-degenerate parabolic equations. We modify Matano’s method
Phillipo Lappicy, Ester Beatriz
semanticscholar +1 more source
A priori estimate of the solution of the Cauchy problem in the Sobolev classes for discontinuous coefficients of degenerate heat equations [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2022 Partial differential equations of the parabolic type with discontinuous coefficients and the heat equation degenerating in time, each separately, have been well studied by many authors.
U.K. Koilyshov +2 more
doaj +3 more sources
On a viscous fourth-order parabolic equation with boundary degeneracy
Boundary Value Problems, 2022 A viscous fourth-order parabolic equation with boundary degeneracy is studied. By using the variational method, the existence of a time-discrete fourth-order elliptic equation with homogeneous boundary conditions is solved.
Bo Liang +4 more
doaj +1 more source