TITLE

On partial regularity of the borderline solution of semilinear parabolic problems

AUTHOR(S)
Kai-Seng Chou; Shi-Zhong Du; Gao-Feng Zheng
PUB. DATE
October 2007
SOURCE
Calculus of Variations & Partial Differential Equations;Oct2007, Vol. 30 Issue 2, p251
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The global, weak solutions for the semilinear problem (1) introduced in Ni-Sacks-Tavantzis (J. Differ. Eq. 54, 97�120 (1984)) are studied. Estimates on the Hausdorff dimension of their singular sets are found. As an application, it is shown that these solutions must blow up in finite time and become regular eventually when the nonlinearity is supercritical and the domain is convex.
ACCESSION #
25524445

 

Related Articles

  • Problems of control and stabilization of impulsive-control dynamic systems with application to nonholonomic mechanics. Kovalev, A.; Kravchenko, N.; Nespirnyi, V. // Automation & Remote Control;Aug2007, Vol. 68 Issue 8, p1444 

    Consideration was given to the control systems using impulses as admissible actions. For impulses of different orders and degrees, these systems can be reduced to a form accepted in the current theory of impulsive systems. The problems of control and stabilization were formulated for the systems...

  • Application of Feedback Linearization to Tracking and Almost Disturbance Decoupling Control of the AMIRA Ball and Beam System. Chen, C.C.; Chien, T.L.; Wei, C.L. // Journal of Optimization Theory & Applications;May2004, Vol. 121 Issue 2, p279 

    This paper studies the tracking and almost disturbance decoupling problem of the nonlinear AMIRA ball and beam system based on the feedback linearization approach. The main contribution of this study is to construct a controller, under appropriate conditions, such that the resulting closed-loop...

  • Observable space of the nonlinear control system on a homogeneous time scale. Kaparin, Vadim; Kotta, Ülle; Wyrwas, Małgorzata // Proceedings of the Estonian Academy of Sciences;2014, Vol. 63 Issue 1, p11 

    The observability property of the nonlinear system, defined on a homogeneous time scale, is studied. The observability condition is provided through the notion of the observable space. Moreover, the observability filtration and observability indices are defined and the decomposition of the...

  • Global Convergence Properties of Nonlinear Conjugate Gradient Methods with Modified Secant Condition. Yabe, Hiroshi; Takano, Masahiro // Computational Optimization & Applications;Jul2004, Vol. 28 Issue 2, p203 

    Conjugate gradient methods are appealing for large scale nonlinear optimization problems. Recently, expecting the fast convergence of the methods, Dai and Liao (2001) used secant condition of quasi-Newton methods. In this paper, we make use of modified secant condition given by Zhang et al....

  • Admissibility of Trajectories for Control Systems Related by Smooth Mappings. Grasse, Kevin A. // Mathematics of Control, Signals & Systems;Sep2003, Vol. 16 Issue 2/3, p120 

    We examine the problem of relating a pair of nonlinear control systems by a smooth mapping between their state spaces that sends trajectories of one system onto trajectories of the other. This problem is fundamental to certain notions of hierarchical structure or state aggregation for control...

  • Controllability of Mechanical Systems in the Class of Controls Bounded Together with Their Derivatives. Matyukhin, V. I.; Pyatnitskii, E. S. // Automation & Remote Control;Aug2004, Vol. 65 Issue 8, p1187 

    A series of studies concerned with controllability of the nonlinear dynamic mechanical systems such as manipulators, aircraft, or water-craft was continued. For the class of smooth controls which comprises swing-bounded controls with bounded derivatives, a criterion for controllability of...

  • ACTIVE CONTROLLER DESIGN FOR THE ANTI-SYNCHRONIZATION OF HYPERCHAOTIC QI AND HYPERCHAOTIC JHA SYSTEMS. Vaidyanathan, Sundarapandian // International Journal of Instrumentation & Control Systems;Apr2012, Vol. 2 Issue 2, p27 

    This paper derives new results for the anti-synchronization of identical hyperchaotic Qi systems (2008), identical hyperchaotic Jha systems (2007) and non-identical hyperchaotic Qi and hyperchaotic Jha systems. Active nonlinear control is the method adopted to achieve the anti-synchronization of...

  • On the Continuous Dependence of an Almost Periodic Solution of a Nonlinear Control System on a Parameter. Ivanov, A. G. // Differential Equations;Feb2003, Vol. 39 Issue 2, p199 

    Studies the continuity of the dependence of a Bohr almost periodic solution of the nonlinear control system on a measure-valued almost periodic control. Number of properties of the mapping which play an important role in optimal control problems for almost periodic motions under mixed...

  • On a Control Problem. Kvitko, A. N. // Differential Equations;Jun2004, Vol. 40 Issue 6, p789 

    Explains a similar problem for a nonlinear control system. Use of an algorithm in constructing a control function; Substitution of relations (2.4) and (2.5) into system (2.2); Transformation of the variable t.

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sign out of this library

Other Topics