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Page 8116 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
The paper deals with a class of degenerate parabolic fourth-order equations with a nonlinear second-order diffusion term of porous- medium type.  ...  Vladimir Grebenev (Novosibirsk) 2002k:35177 35K65 35B45 35K55 Chen, Cai Sheng [Chen, Cai Sheng'|]; Wang, Ru Yun Global existence of and L~ estimates for solutions for a doubly degenerate parabolic equation  ... 

Page 4116 of Mathematical Reviews Vol. , Issue 96g [page]

1996 Mathematical Reviews  
The analysis is also extended to cover merging problems for the fourth- order lubrication equation.”  ...  Ya Zhe Chen (PRC-BJ; Beijing) 96g:35108 35K65 35K55 Wang, Shi Xiang; Lii, Xian Rui (PRC-JIL; Changchun) A note on the existence of classical solutions for a nonlinear degenerate parabolic equation.  ... 

Weak Solution of a Doubly Degenerate Parabolic Equation [article]

Di Kang, Tharathep Sangsawang, Jialun Zhang
2017 arXiv   pre-print
This paper studies a fourth-order, nonlinear, doubly-degenerate parabolic equation derived from the thin film equation in spherical geometry.  ...  The main result of this paper is to prove the existence of a weak solution of the equation in a weighted Sobolev space.  ...  Equation (2) is somewhat similar to equation (1). However, (2) loses its parabolicity at x = ±1 or when u = 0, which makes it a doubly-degenerate parabolic equation.  ... 
arXiv:1610.06303v2 fatcat:d2bv63ybunhw7okgfau6xwl3nu

Page 6113 of Mathematical Reviews Vol. , Issue 92k [page]

1992 Mathematical Reviews  
A. (NL-LEID); Williams, S. M. Source type solutions of a fourth order nonlinear degenerate parabolic equation. Nonlinear Anal. 18 (1992), no. 3, 217-234.  ...  In the doubly degenerate case (m > 2, a > 0), the author has his own contribution for the behaviour of the generalised solution in the cylinder Q7 in some previous papers; in the present one, he studies  ... 

TRAVELLING WAVE SOLUTIONS FOR DOUBLY DEGENERATE REACTION–DIFFUSION EQUATIONS

M. B. A. MANSOUR
2010 ANZIAM journal (Print)  
This paper concerns a nonlinear doubly degenerate reaction-diffusion equation which appears in a bacterial growth model and is also of considerable mathematical interest.  ...  A travelling wave analysis for the equation is carried out. In particular, the qualitative behaviour of both sharp and smooth travelling wave solutions is analysed.  ...  The main purpose of this paper is to perform a travelling wave analysis of the general model equation (1.1) involving doubly degenerate diffusion term, and to give a more complete picture of the travelling  ... 
doi:10.1017/s144618111100054x fatcat:ocjxlnpet5gftior3kmzykr7ui

Travelling wave solutions for doubly degenerate reaction-diffusion equations

Mahmoud Bakheet Ali Mansour
2011 ANZIAM Journal  
This paper concerns a nonlinear doubly degenerate reaction-diffusion equation which appears in a bacterial growth model and is also of considerable mathematical interest.  ...  A travelling wave analysis for the equation is carried out. In particular, the qualitative behaviour of both sharp and smooth travelling wave solutions is analysed.  ...  The main purpose of this paper is to perform a travelling wave analysis of the general model equation (1.1) involving doubly degenerate diffusion term, and to give a more complete picture of the travelling  ... 
doi:10.21914/anziamj.v52i0.3298 fatcat:5rhx7jlj7jhhdirqzye4qvhsfe

Page 6678 of Mathematical Reviews Vol. , Issue 96k [page]

1996 Mathematical Reviews  
Elena Comparini (1-FRNZ; Florence) 96k:35098 35K60 35D05 35R05 Gan, Xiaoqing (PRC-NCH-BC; Nanchang) Existence of weak solution for a doubly degenerate parabolic equation with Radon measures as data.  ...  [Troy, William C.] (1-PITT; Pittsburgh, PA) Stationary solutions of a fourth-order nonlinear diffusion equation. (Russian. Russian summary) Translated from the English by V. V. Kurt.  ... 

Page 9185 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
Summary: “We prove the occurrence of a waiting time phenome- non for solutions to fourth-order degenerate parabolic differential equations which model the evolution of thin films of viscous flu- ids.  ...  (0,7; L'(R%)) such that Existence of a weak solution to problem (1) is shown by J. Filo [Panamer. Math. J. 4 (1994), no. 3, 1-31; MR 95h:35120].  ... 

Page 5771 of Mathematical Reviews Vol. , Issue 86m [page]

1986 Mathematical Reviews  
Rudolf Gorenflo (Berlin) Hoff, David (1-IN) 86m:65108 A scheme for computing solutions and interface curves for a doubly-degenerate parabolic equation. SIAM J. Numer. Anal. 22 (1985), no. 4, 687-712.  ...  The author describes a notion of stability he calls “uniform” and states it to be equiv- alent to A-stability. For evolution equations of second order a partial result is announced.  ... 

The limit of vanishing viscosity for doubly nonlinear parabolic equations

Ales Matas, Jochen Merker
2014 Electronic Journal of Qualitative Theory of Differential Equations  
We show that solutions of the doubly nonlinear parabolic equation ∂b (u) ∂t − div(a(∇u)) + div( f (u)) = g converge in the limit 0 of vanishing viscosity to an entropy solution of the doubly nonlinear  ...  The aim of this article is to prove convergence of the solutions u of the parabolic equation (1.2) to an entropy solution u of the hyperbolic equation (1.1) as 0.  ...  Acknowledgements We would like to thank the reviewers for their valuable suggestions. The authors were supported by the Ministry of Education of the Czech Republic, Research Plan ME10093,2010-2012.  ... 
doi:10.14232/ejqtde.2014.1.8 fatcat:gx2vcau7ffgpbbxd4jdqlspuca

Strong solutions of the thin film equation in spherical geometry [article]

Roman M. Taranets
2017 arXiv   pre-print
This equation can be classified as a doubly degenerate fourth-order parabolic and it models coating flow on the outer surface of a sphere.  ...  We study existence and long-time behaviour of strong solutions for the thin film equation using a priori estimates in a weighted Sobolev space.  ...  Introduction In this paper, we study the following doubly degenerate fourth-order parabolic equation u t + (1 − x 2 )|u| n ((1 − x 2 )u x ) xx x = 0 in Q T , (1.1) where Q T = Ω × (0, T ), n > 0, T > 0  ... 
arXiv:1709.10496v1 fatcat:kzerhgfrmjcjpmps73gwczao7e

Page 3850 of Mathematical Reviews Vol. , Issue 2001F [page]

2001 Mathematical Reviews  
(369-384); Domingo Alberto Tarzia, Explicit solutions to some free boundary problems for the heat equation (385-398); José Miguel Urbano, A singular-degenerate parabolic problem: regu- larity up to the  ...  The fourth chapter focuses on establishing a unified theory for the solution of the radiative transfer equation in enclosures.  ... 

Long-time behaviour and stability for quasilinear doubly degenerate parabolic equations of higher order [article]

Jonas Jansen, Christina Lienstromberg, Katerina Nik
2022 arXiv   pre-print
We study the long-time behaviour of solutions to quasilinear doubly degenerate parabolic problems of fourth order.  ...  Moreover, we can give a detailed picture of the long-time behaviour of solutions with respect to the H^1(Ω)-norm.  ...  JJ and CL have been partially supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the collaborative research centre 'The mathematics of emerging effects' (CRC 1060  ... 
arXiv:2204.08231v1 fatcat:25xtdkj5hvgldnop4w6pyjjaji

Long-time asymptotics and regularity estimates for weak solutions to a doubly degenerate thin-film equation in the Taylor-Couette setting [article]

Christina Lienstromberg, Juan J.L. Velázquez
2022 arXiv   pre-print
We study the dynamic behaviour of solutions to a fourth-order quasilinear degenerate parabolic equation for large times arising in fluid dynamical applications.  ...  In addition, we provide regularity estimates for general nonlinear degenerate parabolic equations of fourth order.  ...  The partial differential equation in (2.1) is quasilinear, of fourth order and (doubly) degenerate parabolic in the sense that we loose parabolicity if either ℎ = 0 or ℎ + 3 ℎ = 0.  ... 
arXiv:2203.00075v1 fatcat:mpicggltcvd4zcemlmaorx7a5a

List of contents

2003 Applied Mathematics Letters  
a Graph Existence and Nonexistence of Global Solutions of Some Nonlocal Degenerate Parabolic Equations NUMBER6 809 A Simple Proof of the Triangle Inequality for the NTV Metric 8 15 Asymptotics  ...  Condition for the Existence of Positive Solutions of Fourth-Order Singular Boundary Value Problems Energy Conservation Property of MW-CRF Determinis-tic Particle Method 293 Large Decription  ... 
doi:10.1016/s0893-9659(03)90138-8 fatcat:sgh4wgebmnfchpedljenuojy2m
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