On some degenerate parabolic equations II [PDF]
Nagoya Mathematical Journal, 1973 In the article I: [8], we have proved the hypoellipticity of a degenerate parabolic equation of the form:where the coefficients a(x, t), b(x,t) and c(x, t) are complex valued smooth functions. The fundamental assumption on the coefficients is that Re a(x, t) satisfies the condition of Nirenberg and Treves ([8], (1.5)).
Tadato Matsuzawa
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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, 2020 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 +5 more
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Null controllability of degenerate parabolic equation with memory [PDF]
Mathematical Methods in the Applied Sciences, 2020 In this paper, we analyze the null controllability property for a degenerate parabolic equation involving memory terms with a locally distributed control. We first derive a null controllability result for a nonhomogeneous degenerate heat equation via new
Brahim Allal, G. Fragnelli
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Regularity and geometric character of solution of a degenerate parabolic equation
Bulletin of Mathematical Sciences, 2016 This work studies the regularity and the geometric significance of solution of the Cauchy problem for a degenerate parabolic equation $$u_{t}=\Delta {}u^{m}$$ u t = Δ u m . Our main objective is to improve the H $$\ddot{o}$$ o ¨ lder estimate obtained by
Jiaqing Pan
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Admissible conditions for parabolic equations degenerating at infinity [PDF]
St. Petersburg Mathematical Journal, 2008 From the introduction: We investigate existence and uniqueness for bounded solutions of the parabolic Cauchy problem \[ \begin{aligned} \rho\partial_tu= \Delta u\quad &\text{in }\mathbb{R}^n\times \mathbb{R}_+:= S,\\ u= u_0\quad &\text{in }\mathbb{R}^n\times \{0\}\;(n\geq 3).\end{aligned}\tag{1.1} \] Concerning the coefficient \(\rho= \rho(x)\) and the
S. Kamin +2 more
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Unique continuation and approximate controllability for a degenerate parabolic equation [PDF]
arXiv.org, 2011 This article studies unique continuation for weakly degenerate parabolic equations in one-space dimension. A new Carleman estimate of local type is obtained to deduce that all solutions that vanish on the degeneracy set, together with their conormal ...
Piermarco Cannarsa +2 more
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Continuous dependence estimate for a degenerate parabolic–hyperbolic equation with Lévy noise [PDF]
, 2016 In this article, we are concerned with a multidimensional degenerate parabolic–hyperbolic equation driven by Lévy processes. Using bounded variation (BV) estimates for vanishing viscosity approximations, we derive an explicit continuous dependence ...
Ujjwal Koley +2 more
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Fractional Sobolev regularity for solutions to a strongly degenerate parabolic equation [PDF]
Forum mathematicum, 2022 We carry on the investigation started in [P. Ambrosio and A. Passarelli di Napoli, Regularity results for a class of widely degenerate parabolic equations, preprint 2022, version 3, https://arxiv.org/abs/2204.05966v3] about the regularity of weak ...
Pasquale Ambrosio
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Strong Traces to Degenerate Parabolic Equations [PDF]
SIAM Journal on Mathematical Analysis, 2022 We prove existence of strong traces at $t=0$ for quasi-solutions to (multidimensional) degenerate parabolic equations with no non-degeneracy conditions. In order to solve the problem, we combine the blow up method and a strong precompactness result for quasi-solutions to degenerate parabolic equations with the induction argument with respect to the ...
Marko Erceg, Darko Mitrović
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The inverse problem with free boundary for a weakly degenerate parabolic equation [PDF]
, 2012 N. M. Hryntsiv
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