Results 221 to 230 of about 5,866 (254)

Maximum Principle for Nonlinear Parabolic Equations

Journal of Mathematical Sciences, 2018
In this paper, the author gives some maximum principles for solutions of some nonlinear parabolic equations. The author considers first, the parabolic equation \[ \mathcal{L}u-u_{t}=f(x,t,u,Du),\text{ in }\Omega\cup\gamma\Omega\tag{1} \] where {\parindent=6mm \begin{itemize}\item[{\(\bullet\)}] \(\Omega\subset\mathbb{R}^n\times(0,\infty)\) is an ...
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Nonlinear Parabolic Equations

1996
We begin this chapter with some general results on the existence and regularity of solutions to semilinear parabolic PDE, first treating the pure initial-value problem in § 1, for PDE of the form $$\frac{\partial u} {\partial t} = Lu + F(t,x,u,\nabla u),\quad u(0) = f,$$ (0.1) where u is defined on [0, T) × M, and M has no boundary.
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Corrected Operator Splitting for Nonlinear Parabolic Equations

SIAM Journal on Numerical Analysis, 2000
The paper concerns a corrected operator splitting method for solving nonlinear parabolic equations of convection-diffusion type. It is shown that the method generates a compact sequence of approximate solutions which converges to the solution of the problem.
Kenneth Hvistendahl Karlsen, Nils Henrik Risebro   +1 more
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Global Attractor of One Nonlinear Parabolic Equation

Ukrainian Mathematical Journal, 2003
Let \(\Omega \) be a domain in \(\mathbb R^n\) with smooth boundary \(\partial \Omega \), \(\Omega_T:=[0,T]\times \Omega \). The authors consider the Cauchy-Dirichlet problem \[ \begin{gathered} u_t=a\Delta u-f(u)+\lambda u+\langle {\mathbf b}({\mathbf x}),\nabla u \rangle -g({\mathbf x});\tag{1} \\ u\big|_{\partial \Omega}=0,\quad u\big|_{t=0}=u_0 ...
Kapustyan, O. V., Shkundin, D. V.
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Asymptotic Behavior of the Nonlinear Parabolic Equations

Journal of Partial Differential Equations, 2004
Summary: This paper is concerned with the large time behavior for solutions of the nonlinear parabolic equations in the whole space \(\mathbb{R}^n\). The spectral decomposition methods of the Laplace operator are applied and it is proved that if the initial data \(u_0\in L^2\cap L^r\) for \(1\leq r\leq 2\), then the solutions decay in \(L^2\) norm at \(
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Dynamics of Nonlinear Parabolic Equations with Cosymmetry

2007
Dynamics of a cosymmetric system of nonlinear parabolic equations is studied to model of population kinetics. Computer algebra system Maple is applied to perform some stages of analytical investigation and develop a finite-difference scheme which respects the cosymmetry property.
Ekaterina S. Kovaleva, Vyacheslav Tsybulin, Kurt Frischmuth   +2 more
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Nonlinear parabolic equations for measures

St. Petersburg Mathematical Journal, 2012
Summary: A new existence result is established for weak parabolic equations for probability measures. Sufficient conditions are given for the existence of local and global-in-time probability solutions of the Cauchy problem for such equations. Some conditions under which global-in-time solutions do not exist are indicated.
Manita, O. A., Shaposhnikov, S. V.
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Some degenerate nonlinear parabolic equations

九州大学教養部数学雑誌, 1984
The author proves existence, uniqueness and asymptotic behaviour of solutions of the initial value problem for the generalized porous medium equation on a bounded domain in \({\mathbb{R}}^ n\). In various cases, decay notes, positivity and uniqueness are given which extend known results in various directions.
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On some parabolic equations with mon ditferentiable nonlinearities

Communications in Partial Differential Equations, 1982
(1982). On some parabolic equations with mon ditferentiable nonlinearities. Communications in Partial Differential Equations: Vol. 7, No. 12, pp. 1439-1452.
DE MOTTONI P, SCHIAFFINO A, TESEI, Alberto   +2 more
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Parabolic equations with operator nonlinearity

Asian-European Journal of Mathematics
In this paper, we consider partial differential equations (PDE) of parabolic type with functional nonlinearity in the reaction summand. Our goal is to give the answer of the question if there exist a set of smooth functions satisfying the inequality [Formula: see text], where [Formula: see text] is a parabolic operator in the parabolic PDE with a ...
Saba Iftikhar, Alina Lazu, Tzanko Donchev, Nikolay Kitanov, Dimitar Kolev   +4 more
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