Regularity and geometric character of solution of a degenerate parabolic equation
Bulletin of Mathematical Sciences, 2015 This work studies the regularity and the geometric significance of solution of the Cauchy problem for a degenerate parabolic equation $u_{t}=\Delta{}u^{m}$.
Pan, Jiaqing
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Gaussian bounds for degenerate parabolic equations
Journal of Functional Analysis, 2008 AbstractLet A be a real symmetric, degenerate elliptic matrix whose degeneracy is controlled by a weight w in the A2 or QC class. We show that there is a heat kernel Wt(x,y) associated to the parabolic equation wut=divA∇u, and Wt satisfies classic Gaussian bounds:|Wt(x,y)|⩽C1tn/2exp(−C2|x−y|2t).
David Cruz-Uribe, Cristian Rios
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Degenerate semilinear parabolic equations [PDF]
Differential and Integral Equations, 1992 Andreas Stahel
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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
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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 $$\begin{aligned} u_t-\textrm{div}\left( \left( \left| Du\right| -1\right) _+^{p-1}\frac{Du}{\left| Du\right ...
Andrea Gentile +1 more
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Convergence of Inverse Volatility Problem Based on Degenerate Parabolic Equation
Mathematics, 2022 Based on the theoretical framework of the Black–Scholes model, the convergence of the inverse volatility problem based on the degenerate parabolic equation is studied.
Yilihamujiang Yimamu, Zuicha Deng
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Carleman estimates for a stochastic degenerate parabolic equation and applications to null controllability and an inverse random source problem [PDF]
Inverse Problems, 2019 In this paper, we establish two Carleman estimates for a stochastic degenerate parabolic equation. The first one is for the backward stochastic degenerate parabolic equation with singular weight function.
Bin Wu, Qun Chen, Zewen Wang
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Saturated Fronts in Crowds Dynamics
Advanced Nonlinear Studies, 2021 We consider a degenerate scalar parabolic equation, in one spatial dimension, of flux-saturated type. The equation also contains a convective term. We study the existence and regularity of traveling-wave solutions; in particular we show that they can be ...
Campos Juan +2 more
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Existence and cost of boundary controls for a degenerate/singular parabolic equation [PDF]
Mathematical Control and Related Fields, 2020 In this paper, we consider the following degenerate/singular parabolic equation $$ 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
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Existence results for some nonlinear parabolic equations with degenerate coercivity and singular lower-order terms [PDF]
Mathematica Bohemica, 2023 In this paper, we study the existence results for some parabolic equations with degenerate coercivity, singular lower order term depending on the gradient, and positive initial data in $L^1$.
Rabah Mecheter, Fares Mokhtari
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