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On Solutions of Semilinear Parabolic Equations
On Solutions of Semilinear Parabolic Equationsopenaire
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IDENTIFICATION OF PARAMETERS IN SEMILINEAR PARABOLIC EQUATIONS
Acta Mathematica Scientia, 1999Summary: 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.
Zhenhai Liu
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Lifespan for a semilinear pseudo‐parabolic equation
Mathematical Methods in the Applied Sciences, 2017This paper deals with the blow‐up solution to the following semilinear pseudo‐parabolic equation urn:x-wiley:mma:media:mma4639:mma4639-math-0001 in a bounded domain , which was studied by Luo (Math Method Appl Sci 38(12):2636‐2641, 2015) with the following assumptions on p: urn:x-wiley:mma:media:mma4639:mma4639-math-0003 and the lifespan for the ...
Guangyu Xu, Jun Zhou
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Stabilisation of parabolic semilinear equations
International Journal of Control, 2016ABSTRACTWe 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 ...
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GLOBAL SOLUTION OF A SEMILINEAR PARABOLIC EQUATION
Acta Mathematica Scientia, 1991The 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
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Optimal Control of Nonsmooth, Semilinear Parabolic Equations
SIAM Journal on Control and Optimization, 2017This 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
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THE EXISTENCE AND THE UNIQUENESS OF A SEMILINEAR PARABOLIC EQUATION
Acta Mathematica Scientia, 1985The 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.
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Stabilizing Semilinear Parabolic Equations
Numerical Functional Analysis and Optimization, 2005In 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
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HOMOGENIZATION OF SEMILINEAR PARABOLIC EQUATIONS IN PERFORATED DOMAINS
Chinese Annals of Mathematics, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Donato, P., Nabil, A.
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W-methods for semilinear parabolic equations
Applied Numerical Mathematics, 1995The 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
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