Results 221 to 230 of about 2,128,627 (261)

Nonlinear Degenerate Parabolic Equations with a Singular Nonlinearity

Acta Applicandae Mathematicae
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Hichem Khelifi, Fares Mokhtari
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On the Solutions of the Coupled Nonlinear Parabolic Equations

Journal of Partial Differential Equations, 1996
By means of the fixed point technique and integral estimation method, we study the solutions of periodic boundary value problem and initial value problem for the coupled nonlinear parabolic equations. The global classical solutions of the mentioned problems are shown to exists.
Shen, Longjun, Zhang, Linghai
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Parabolic equations with double variable nonlinearities

Mathematics and Computers in Simulation, 2011
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Stanislav N. Antontsev, Sergey Shmarev
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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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Nonlinear Degenerate Parabolic Equation with Nonlinear Boundary Condition

Acta Mathematica Sinica, English Series, 2005
The authors study the existence and nonexistence of global positive solutions to the following nonlinear parabolic equation with nonlinear boundary conditions \[ \begin{aligned} & (u^k)_t = \Delta_mu,\quad x \in\Omega, \quad t > 0,\\ & \nabla_m u\cdot\nu = u^{\alpha},\quad x\in \partial\Omega, \quad t > 0,\\ & u(x,0) = u_0(x),\quad x\in\bar\Omega, \end{
Sun, Wenjun, Wang, Shu
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Estimates for nonlinear parabolic equations.

2000
Summary: We study smooth non-negative solutions of the equation \(u_t=\partial_j a_j(u,\nabla u)+a_0(u,\Delta u)\) in the strip \(S_T= \mathbb{R}^d\times (0,T)\), \(d\geq 1\). A regularizing effect, pointwise estimates and gradient estimates are obtained.
Fabricant, A., Marinov, M., Rangelov, T.
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On the oscillations of solutions of nonlinear parabolic equations

Applied Mathematics and Computation, 2003
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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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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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Corrected Operator Splitting for Nonlinear Parabolic Equations

SIAM Journal on Numerical Analysis, 2000
We present a corrected operator splitting (COS) method for solving nonlinear parabolic equations of a convection-diffusion type. The main feature of this method is the ability to correctly resolve nonlinear shock fronts for large time steps, as opposed to a standard operator splitting (OS) which fails to do so.
Kenneth Hvistendahl Karlsen, Nils Henrik Risebro   +1 more
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