Results 21 to 30 of about 1,264,456 (207)
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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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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A Picone identity for variable exponent operators and applications
Advances in Nonlinear Analysis, 2019 In this work, we establish a new Picone identity for anisotropic quasilinear operators, such as the p(x)-Laplacian defined as div(|∇ u|p(x)−2 ∇ u).
Arora Rakesh +2 more
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On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation [PDF]
Discrete Dynamics in Nature and Society, 2009 By Oleinik′s line method, we study the existence and the uniqueness of the classical solution of the Cauchy problem for the following equation in [0, T] × R2: ∂xxu + u∂yu − ∂tu = f(⋅, u), provided that T is suitable small. Results of numerical experiments are reported to demonstrate that the strong solutions of the above equation may blow up in ...
Zongqi Liang, Huashui Zhan
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Large time behavior in a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system [PDF]
, 2022 summary:This paper deals with a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system. Boundedness, stabilization and blow-up in this system of the fully parabolic and parabolic-elliptic-elliptic versions have already been ...
Chiyo, Yutaro +2 more
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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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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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The quasilinear parabolic kirchhoff equation
Open Mathematics, 2017 Abstract In this paper the existence of solution of a quasilinear generalized Kirchhoff equation with initial – boundary conditions of Dirichlet type will be studied using the Leray – Schauder principle.
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On maximal parabolic regularity for non-autonomous parabolic operators [PDF]
, 2016 We consider linear inhomogeneous non-autonomous parabolic problems associated to sesquilinear forms, with discontinuous dependence of time. We show that for these problems, the property of maximal parabolic regularity can be extrapolated to time ...
ter Elst, A. F. M. +9 more
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Removable isolated singularities for solutions of quasilinear parabolic equations [PDF]
, 2009 We have obtained the best possible conditions for removable singularity at the point for solutions of quasilinear parabolic equations of divergent ...
Nicolosi, F. +2 more
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