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Quasilinear evolution equations and parabolic systems [PDF]
Transactions of the American Mathematical Society, 1986 It is shown that general quasilinear parabolic systems possess unique maximal classical solutions for sufficiently smooth initial values, provided the boundary conditions are “time-independent”. Moreover it is shown that, in the autonomous case, these equations generate local semiflows on appropriate Sobolev spaces. Our results apply, in particular, to
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Computing optimal control with a quasilinear parabolic partial differential equation [PDF]
Surveys in Mathematics and its Applications, 2009 This paper presents the numerical solution of a constrained optimal control problem (COCP) for quasilinear parabolic equations. The COCP is converted to unconstrained optimization problem (UOCP) by applying the exterior penalty function method. Necessary
M. H. Farag
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International Journal of Mathematics and Mathematical Sciences, 1987 Optimal error estimates in L2, H1 and H2-norm are established for a single phase Stefan problem with quasilinear parabolic equation in non-divergence form by an H1-Galerkin procedure.
A. K. Pani, P. C. Das
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Filtration in cohesive soils: numerical approach
Computer Assisted Methods in Engineering and Science, 2023 Paper presents a numerical method for solving the initial boundary-value problem for a certain quasilinear parabolic equation describing the low velocity filtration problem. The convergence of the method is proved.
Robert Schaefer, Stanislaw Sędziwy
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Parabolic regularization of the gradient catastrophes for the Burgers-Hopf equation and Jordan chain
, 2018 Non-standard parabolic regularization of gradient catastrophes for the Burgers-Hopf equation is proposed. It is based on the analysis of all (generic and higher order) gradient catastrophes and their step by step regularization by embedding the Burgers ...
Konopelchenko, B. G., Ortenzi, G.
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Abstract and Applied Analysis, 2003 This paper deals with weak solution in weighted Sobolev spaces, of three-point boundary value problems which combine Dirichlet and integral conditions, for linear and quasilinear parabolic equations in a domain with curved lateral boundaries. We, firstly,
Abdelfatah Bouziani
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, 2013 We study the relative value iteration for the ergodic control problem under a near-monotone running cost structure for a nondegenerate diffusion controlled through its drift.
Arapostathis, Ari +2 more
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On well-posedness, stability, and bifurcation for the axisymmetric surface diffusion flow [PDF]
, 2013 In this article, we study the axisymmetric surface diffusion flow (ASD), a fourth-order geometric evolution law. In particular, we prove that ASD generates a real analytic semiflow in the space of (2 + \alpha)-little-H\"older regular surfaces of ...
Amann H. +25 more
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Journal of Optimization, Differential Equations and Their Applications, 2023 In this work, we study a sparse optimal control problem involving a quasilinear parabolic equation with variable order of nonlinearity as a state equation and with a pointwise control constraints.
Ciro D’Apice +2 more
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Uniform Bounds for Solutions to Quasilinear Parabolic Equations
Journal of Differential Equations, 2001 The authors consider a class of quasilinear parabolic equations on a domain \(D \subset \mathbb{R}^d\) of finite Lebesgue measure in the form \[ u_t(t,x) = \text{div\,} a(t,x,u(t,x), \nabla u(t,x)); \quad t \in (0,\infty),\;x \in D. \] where \(a : (0,\infty)\times D \times \mathbb{R} \times \mathbb{R}^d \to \mathbb{R}^d\) is a Carathéodory function ...
CIPRIANI, FABIO EUGENIO GIOVANNI +1 more
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