Results 21 to 30 of about 1,241 (227)

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
doaj  

On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification

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
doaj   +1 more source

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
doaj   +1 more source

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, GRILLO, GABRIELE   +1 more
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Optimal control of quasilinear parabolic equations [PDF]

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1995
This paper deals with optimal control problems governed by quasilinear parabolic equations in divergence form, whose cost functional is of Lagrangian type. Our aim is to prove the existence of solutions and derive some optimality conditions. To attain this second objective, we accomplish the sensitivity analysis of the state equation with respect to ...
Casas, Eduardo, Fernández, Luis A., Yong, Jiongmin   +2 more
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Abstract quasilinear parabolic equations

Mathematische Annalen, 1984
The author deals with an abstract quasilinear parabolic problem \(u'(t)=A(t,u(t))u(t)+f(t,u(t)), t>0\), \(u(0)=u_ 0\) in a Banach space X. His theorems on existence and uniqueness are such that a concrete quasilinear parabolic problem can be attacked without imposing growth conditions on the coefficients.
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Quasilinear parabolic stochastic partial differential equations: Existence, uniqueness

Stochastic Processes and their Applications, 2017
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 monotone.
Hofmanová, Martina, Zhang, Tusheng
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Global Sobolev Solutions of Quasilinear Parabolic Equations

Differential and Integral Equations, 1998
Global existence, uniqueness and a priori estimates of solutions to the initial and homogeneous Dirichlet boundary value problem for the equation \[ u_t - \sum _{i,j=1}^{n} a_{i,j}(\nabla u) \partial _i \partial _j u = f(x,t)\quad\text{on} \Omega \times (0,T) \] is proved in Sobolev spaces \(X_{s+2}(T)\) for sufficiently large \(s.\) Here \[ X_m(T) = \{
McLeod, Kevin, Milani, Albert
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Influence of Competitive C–P Segregation on Austenite Grain Growth in Iron Alloys

steel research international, Volume 97, Issue 3, Page 1432-1443, March 2026.
This study investigates how carbon influences phosphorus‐induced solute drag effects during isothermal annealing of austenite grain growth in Fe–C–P alloys. Using in situ high‐temperature laser scanning confocal microscopy and density functional theory simulations, it demonstrates that carbon above a critical temperature significantly reduces P ...
Maximilian Kern, Michael Bernhard, Daniel Scheiber, Matthias Militzer, Christian Bernhard   +4 more
wiley   +1 more source