Results 151 to 160 of about 243 (185)

On the Asymptotic Behavior of Solutions of Semilinear Parabolic Equations

SIAM Journal on Applied Mathematics, 1975
Let u be a solution of a second order semilinear parabolic equation which satisfies either Dirichlet or mixed boundary conditions. Let v be a stationary solution of this problem. Then by substituting $u = v + \varepsilon w$, and omitting terms of higher order in $\varepsilon $ than $O( \varepsilon )$, we may formally derive a linear problem.
Ewer, J. P. G., Peletier, L. A.
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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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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 ...
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Numerical Methods for Semilinear Parabolic Equations

SIAM Journal on Numerical Analysis, 1987
The parabolic problem: (1) \(u_ t-\nabla \cdot (D(\chi,t)\nabla u)=f(\chi,t,u)\) for \(x\in \Omega\), \(0\leq t\leq T\); \(\alpha (\chi_ 0)\partial u/\partial \nu +\beta (\chi_ 0)u=h(\chi_ 0,t)\) for \(\chi_ 0\in \partial \Omega\), \(0\leq t\leq T\), and \(u(0,\chi)=\psi (\chi)\) for \(\chi\in \Omega\) is approximated in the usual way by an implicit ...
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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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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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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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Dimension of a central manifold for semilinear parabolic equations

Ukrainian Mathematical Journal, 1990
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The boundary quenching behavior of a semilinear parabolic equation

Applied Mathematics and Computation, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An inverse problem for a semilinear parabolic equation

Annali di Matematica Pura ed Applicata, 1982
In this paper we are concerned with the study of the stability of an unknown non-linear term in a parabolic equation in dependence on over specified Cauchy-Dirichlet data prescribed on the parabolic boundary of the open set under consideration. Since, in general, the dependence of the nonlinear term upon the data is not stable with respect to L ...
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