Results 21 to 30 of about 12,675 (193)
On quasilinear parabolic evolution equations in weighted Lp-spaces II [PDF]
, 2013 Our study of abstract quasi-linear parabolic problems in time-weighted L_p-spaces, begun in [17], is extended in this paper to include singular lower order terms, while keeping low initial regularity.
D. Bothe +6 more
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Stability of solutions of quasilinear parabolic equations
Journal of Mathematical Analysis and Applications, 2005 We bound the difference between solutions $u$ and $v$ of $u_t = aΔu+\Div_x f+h$ and $v_t = bΔv+\Div_x g+k$ with initial data $ϕ$ and $ ψ$, respectively, by $\Vert u(t,\cdot)-v(t,\cdot)\Vert_{L^p(E)}\le A_E(t)\Vert ϕ-ψ\Vert_{L^\infty(\R^n)}^{2ρ_p}+ B(t)(\Vert a-b\Vert_{\infty}+ \Vert \nabla_x\cdot f-\nabla_x\cdot g\Vert_{\infty}+ \Vert f_u-g_u\Vert_ ...
COCLITE, Giuseppe Maria, HOLDEN H.
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Parabolic equations with dynamical boundary conditions and source terms on interfaces [PDF]
, 2012 We consider parabolic equations with mixed boundary conditions and domain inhomogeneities supported on a lower dimensional hypersurface, enforcing a jump in the conormal derivative.
Meyries, Martin +2 more
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Smooth Solutions of systems of quasilinear parabolic equations [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2002 Diagonal quasilinear parabolic systems arising in the context of stochastic differential games are considered: \[ \partial_t u^k- (a_{ij}(x,t)u^k_{x_j})_{x_i} = H^k(x,t,u,\nabla u) , \] where the Hamiltonians \(H^k\) have quadratic growth in \(\nabla u\). Uniform ellipticity of \(a_{ij}\) and special structure conditions \[ | H^k(x,t,u,p)| \leq C | p^k|
Bensoussan, Alain, Frehse, Jens
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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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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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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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