Results 161 to 170 of about 12,988 (199)

Dimension splitting for quasilinear parabolic equations

IMA Journal of Numerical Analysis, 2009
In the current paper, we derive a rigorous convergence analysis for a broad range of splitting schemes applied to abstract nonlinear evolution equations, including the Lie and Peaceman-Rachford splittings. The analysis is in particular applicable to (possibly degenerate) quasilinear parabolic problems and their dimension splittings.
E. Hansen, A. Ostermann
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Cauchy’s Problem for Degenerate Quasilinear Parabolic Equations

Theory of Probability & Its Applications, 1964
In this paper we consider the differential properties of the solution to the Cauchy problem for the quasilinear parabolic equation \[ (1)\qquad \frac{{\partial v}}{{\partial t}} = \frac{1}{2}\sum\limits_{i,j = 1}^n {c_{ij} } (t,x,v)\frac{{\partial ^2 v}}{{\partial x_i \partial x_i }} + \sum\limits_{i = 1}^n {a_i } (t,x,v)\frac{{\partial v}}{{\partial ...
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Generalized Quasilinearization for Quasilinear Parabolic Equations with Nonlinearities of DC Type

Journal of Optimization Theory and Applications, 2001
The authors consider an initial-boundary value problem for a class of quasilinear parabolic equations whose lower-order nonlinearity is of d.c. function type (difference of two convex functions) with respect to the dependent variable. Combining the method of quasilinearization with the well-known method of upper and lower solutions together with the ...
Carl, S., Lakshmikantham, V.
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Quasilinear Parabolic Equations in Lp

2006
The paper contains a local existence and uniqueness result for quasilinear parabolic equations on a three-dimensional domain including mixed boundary conditions and discontinuous coefficients.
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Local Solutions of Weakly Parabolic Quasilinear Differential Equations

Mathematische Nachrichten, 1999
AbstractWe consider a quasilinear parabolic boundary value problem, the elliptic part of which degenerates near the boundary. In order to solve this problem, we approximate it by a system of linear degenerate elliptic boundary value problems by means of semidiscretization with respect to time.
Dreher, Michael, Pluschke, Volker
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Dynamic theory of quasilinear parabolic equations—I. Abstract evolution equations

Nonlinear Analysis: Theory, Methods & Applications, 1988
The author studies the qualitative properties of the solutions v of an abstract ordinary differential equation of the form \[ (1)\quad v'+A(t,v)v=F(t,v), \] where A(t,v) is the infinitesimal generator of an analytic semigroup in a Banach space. Under suitable Hölder continuity assumptions on A and F, several properties of the solutions v of (1) are ...
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Monotone solutions to quasilinear parabolic equations

Siberian Mathematical Journal, 1993
General quasilinear parabolic equations on a bounded domain in \(\mathbb{R}^ N\) under linear boundary conditions are considered. Due to the maximum principle, the solution flows of such equations belong to the class of strongly monotone (order preserving) dynamical systems.
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Nonlocal Problems for Quasilinear Parabolic Equations

2002
We study a class of quasilinear parabolic equations with nonlocal initial conditions. The initial conditions are a generalization of periodicity with respect to time and include conditions studied by other authors, which can be used to study inverse problems and problems arising in reactor theory.
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Removable Sets for Quasilinear Parabolic Equations

Journal of the London Mathematical Society, 1980
Gariepy, Ronald, Ziemer, William P.
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Colloidal Self-Assembly Approaches to Smart Nanostructured Materials

Chemical Reviews, 2022
Zhiwei Li Li, Yadong Yin
exaly