Results 21 to 30 of about 13,183 (198)
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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Quasilinear parabolic stochastic partial differential equations: existence, uniqueness [PDF]
, 2015 In this paper, we provide a direct approach to the existence and uniqueness of strong (in the probabilistic sense) and weak (in the PDE sense) solutions to quasilinear stochastic partial differential equations, which are neither monotone nor locally ...
Hofmanova, Martina, Zhang, Tusheng
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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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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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Rate of Convergence of Space Time Approximations for stochastic evolution equations [PDF]
, 2007 Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators driven by a finite dimensional Brownian motion are considered.
A. Cohen +14 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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A posteriori error bounds for discontinuous Galerkin methods for quasilinear parabolic problems [PDF]
, 2009 We derive a posteriori error bounds for a quasilinear parabolic problem, which is approximated by the $hp$-version interior penalty discontinuous Galerkin method (IPDG). The error is measured in the energy norm.
Anthonissen, M.J.H. +5 more
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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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Multivalued solutions of multidimensional linear equations of heat conduction and rivertons
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2021 Background. The article considers the problem of calculating multivalued solutions of multidimensional linear parabolic equations. Solutions for this type of equations of heat conductivity in dimension d > 2 were not previously known and represent an ...
V.M. Zhuravlev, V.M. Morozov
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