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Convergence analysis of domain decomposition based time integrators for degenerate parabolic equations. [PDF]
Numer Math (Heidelb), 2018 Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them well-suited for the temporal discretization of parabolic systems, in general, and degenerate parabolic problems, in particular.
Eisenmann M, Hansen E.
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On Degenerate Parabolic Equations [PDF]
International Journal of Mathematics and Mathematical Sciences, 2011 The paper deals with the existence of solutions of some generalized Stefan‐type equation in the framework of Orlicz spaces.
Mohammed Kbiri Alaoui
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Null controllability of degenerate parabolic equation with memory [PDF]
Mathematical Methods in the Applied Sciences, 2021 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 Carleman estimates with weighted time functions that do not blow up at .
Allal, Brahim, Fragnelli, Genni
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Strong Traces to Degenerate Parabolic Equations
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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Stability for degenerate parabolic equations [PDF]
Advances in Calculus of Variations, 2010 in a cylindrical domain. The main question is that do the weak solutions of (1.1) with fixed initial and boundary values converge in any reasonable sense to the solution of the limit problem as p varies. Apart from mathematical interest, the stability questions is motivated by error analysis in applications: It is desirable that solutions remain stable
Parviainen, Mikko, Kinnunen, Juha
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A degenerate pseudo-parabolic equation with memory [PDF]
Communications in Applied and Industrial Mathematics, 2019 Abstract We prove the existence and uniqueness for a degenerate pseudo-parabolic problem with memory. This kind of problem arises in the study of the homogenization of some differential systems involving the Laplace-Beltrami operator and describes the effective behaviour of the electrical conduction in some composite materials.
M. Amar +3 more
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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
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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)).
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Probabilistic approach for systems of second order quasi-linear parabolic PDEs [PDF]
, 2012 Using the stochastic representation for second order parabolic equations, we prove the existence of local smooth solutions in Sobolev spaces for a class of second order quasi-linear parabolic partial differential equations (possibly degenerate) with ...
Wang, Jinxia, Zhang, Xicheng
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Convergence for Degenerate Parabolic Equations
Journal of Differential Equations, 1999 AbstractWe prove that any bounded global solution to a degenerate parabolic problem in one spatial dimension converges to a unique stationary state.
Frédérique Simondon, Eduard Feireisl
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