Results 211 to 220 of about 14,488 (245)

Spectral method for semilinear parabolic integrodifferential equations

Applied Mathematics and Mechanics, 1995
The authors consider the parabolic integro-differential equation: \[ {\partial u\over \partial t} (x,t) + {\partial^2 u\over \partial x^2} (x,t) = \int^t_0 f(t,s,u(x,s))ds \] that is semidiscretized. The trapezoidal rule is adopted for the quadrature of the memory term.
Liu, Xiaoqing, Wu, Shengchang
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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 ...
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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
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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.
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Quenching for degenerate semilinear parabolic equations

Applicable Analysis, 1994
Let q and a be nonzero constants, and for some constant c such that . We show existence of a unique classical solution for the degenerate parabolic differential equation, , subject to the initial condition and the boundary conditionsu . Let . It is established that if M>∞, then the set of quenching points is in for q>0, and in for q>0.
C. Y. Chan, P. C. Kong
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Wave solutions of semilinear parabolic equations

Theoretical and Mathematical Physics, 1991
The paper is concerned with solutions of the type \[ u(x,t)=\chi(\tau)=\chi(x+pt+p_ 0), p,p_ 0 \text{constants} \] of the equation \(u_ t-u_{xx}-F(u)=0\). Interactions of nonlinear waves (kinks), described by semilinear parabolic equations are investigated.
Danilov, V. G., Subochev, P. Yu.
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Removable singularities of semilinear parabolic equations

Proceedings of the American Mathematical Society, 2013
The author studies the removability property for solutions of the semilinear parabolic equation \[ u_t-\Delta u=F(x,t,u,\nabla u) \quad\text{ in }(\Omega\setminus\{0\})\times (0,T), \] where \(\Omega\) is a domain of \({\mathbb R}^n\), (\(n\geq 3\)) containing the origin and \(T>0\). The first result of the paper establishes that if \(F\) satisfies \[ |
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Semilinear Parabolic Equations with Infinite Delay

1985
We shall deal with an abstract semilinear evolution equation $$\dot u\left( t \right) + Au\left( t \right) = F\left( {t,u} \right),{u_0} = \varphi ,$$ (1) with infinite delay, i.e., ut denotes a function ut(s) = u(t+s) on the interval (− ∞, 0]. The motivation for the study of such equations comes partly from theoretical biology.
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Semilinear Parabolic Equations

2021
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Feedback Stabilization of Semilinear Parabolic Equations

2018
We shall discuss here the internal and boundary feedback stabilization of equilibrium solutions to semilinear parabolic equations. The main conclusion is that such an equation is stabilizable by a feedback controller with finite dimensional structure dependent of the unstable spectrum of the corresponding linearized system around the equilibrium ...
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