Results 141 to 150 of about 240 (185)

Stabilisation of parabolic semilinear equations

International Journal of Control, 2016
ABSTRACTWe design here a finite-dimensional feedback stabilising Dirichlet boundary controller for the equilibrium solutions to parabolic equations. These results extend that ones in Barbu (2013), which provide a feedback controller expressed in terms of the eigenfunctions φj corresponding to the unstable eigenvalues {λj}j=1N of the operator ...
openaire   +1 more source

GLOBAL SOLUTION OF A SEMILINEAR PARABOLIC EQUATION

Acta Mathematica Scientia, 1991
The authors consider the semilinear parabolic equation \(u_ t=\Delta u+| u|^{\gamma-1}u-u\), where \((x,t)\in\mathbb{R}^ n\times\mathbb{R}^ +\) \((\gamma>1)\), in the weighted Lebesgue class \(D_ q^ \alpha=\{u\in L_ q:\;| x|^ \alpha u\in L_ q\}\). Existence and asymptotic behaviour results of the global solutions for the associated Cauchy problem with ...
Ding, Xiaxi, Zhao, Huijiang
openaire   +2 more sources

Optimal Control of Nonsmooth, Semilinear Parabolic Equations

SIAM Journal on Control and Optimization, 2017
This paper is concerned with an optimal control problem governed by nonsmooth semilinear parabolic equations. The essential feature of the problem is that the nonlinearity in the state equation is only Lipschitz continuous and not necessarily Gateaux-differentiable.
Christian Meyer, Livia M. Susu
openaire   +2 more sources

THE EXISTENCE AND THE UNIQUENESS OF A SEMILINEAR PARABOLIC EQUATION

Acta Mathematica Scientia, 1985
The author considers the existence and uniqueness of a Cauchy problem of a semilinear parabolic equation (1) \[ u_ t=\Delta u+m_ 0u+k_ 0u \ell n u^ 2\quad in\quad R^ n\times R_+ \] \[ u|_{t=0}=u_ 0(x)\in H^ 1(R^ n)\quad in\quad R^ n, \] where \(k_ 0\geq 0\), \(m_ 0\) are constants.
openaire   +2 more sources

Stabilizing Semilinear Parabolic Equations

Numerical Functional Analysis and Optimization, 2005
In this paper we prove the internal feedback stabilization of steady-state solutions of semilinear parabolic equations and introduce a controller synthesis methodology based on finite element approximations of the original PDEs. Numerical tests are given for some one- and two-dimensional nonlinear parabolic equations.
V. Barbu, D. Coca, Y. Yan
openaire   +1 more source

IDENTIFICATION OF PARAMETERS IN SEMILINEAR PARABOLIC EQUATIONS

Acta Mathematica Scientia, 1999
Summary: An optimization theoretic approach to the estimation of coefficients in a semilinear parabolic equation is presented. It is based on convex analysis techniques. General existence theorems are proved in an \(L^1\) setting. A necessary solvability condition is given.
openaire   +2 more sources

W-methods for semilinear parabolic equations

Applied Numerical Mathematics, 1995
The author studies the temporal convergence behavior of \(W\)-methods applied to the initial value problem \[ u'(t)+ Au(t)= g(t, u(t)), \quad u(t_0) \text{ given}, \] in an arbitrary Banach space \(X\). The operator \(A\) is not necessarily bounded. The stability and convergence analysis uses the framework of analytic semigroups of linear operators and
openaire   +1 more source

HOMOGENIZATION OF SEMILINEAR PARABOLIC EQUATIONS IN PERFORATED DOMAINS

Chinese Annals of Mathematics, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Donato, P., Nabil, A.
openaire   +2 more sources

Semilinear Parabolic Equations

1997
In the last chapter we considered discretization in both space and time of a model nonlinear parabolic equation. The discretization with respect to space was done by piecewise linear finite elements and in time we applied the backward Euler and Crank-Nicolson methods. In this chapter we shall restrict the consideration to the case when only the forcing
openaire   +1 more source

Generalized Solutions of Semilinear Parabolic Equations

Monatshefte für Mathematik, 2005
The Cauchy problem for the semilinear parabolic equation \(u_t=\Delta_x u+f(u)\) in \(t>0\), \(x\in \mathbb R^n\) is studied in the framework of algebra of generalized functions introduced by Colombeau. By using approximations for generalized functions, the results on existence and uniqueness of generalized functions solution are obtained -- in ...
openaire   +1 more source