Well-posedness and stationary solutions [PDF]
, 2011 In this paper we prove existence and uniqueness of variational inequality solutions for a bistable quasilinear parabolic equation arising in the theory of solid-solid phase transitions and discuss its stationary solutions, which can be ...
Grinfeld, Michael, Burns, Martin
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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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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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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
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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
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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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A family of difference schemes for fourth order parabolic partial differential equations [PDF]
, 1983 A family of methods is developed for the numerical solution of fourth order parabolic partial differential equations in one- and two-space variables.
Khaliq, AQM, Twizell, EH
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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.
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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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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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