Nonlocal đť‘ť-Laplacian evolution problems

10.1090/surv/165/06 â—˝  
2010 â—˝  
pp. 123-161
Author(s):  
Fuensanta Andreu-Vaillo â—˝  
José Mazón â—˝  
Julio Rossi â—˝  
J. Julián Toledo-Melero
Keyword(s):  
Evolution Problems

scholarly journals Regularity and time behavior of the solutions to weak monotone parabolic equations

2021 â—˝  
Author(s):  
Maria Michaela Porzio
Keyword(s):  
Heat Equation â—˝  
Parabolic Equations â—˝  
Parabolic Problems â—˝  
Summable Function â—˝  
Time Behavior â—˝  
Decay Estimates â—˝  
Laplacian Equation â—˝  
Evolution Problems â—˝  
Degenerate Equations â—˝  
Uniqueness Results

AbstractIn this paper, we study the behavior in time of the solutions for a class of parabolic problems including the p-Laplacian equation and the heat equation. Either the case of singular or degenerate equations is considered. The initial datum $$u_0$$ u 0 is a summable function and a reaction term f is present in the problem. We prove that, despite the lack of regularity of $$u_0$$ u 0 , immediate regularization of the solutions appears for data f sufficiently regular and we derive estimates that for zero data f become the known decay estimates for these kinds of problems. Besides, even if f is not regular, we show that it is possible to describe the behavior in time of a suitable class of solutions. Finally, we establish some uniqueness results for the solutions of these evolution problems.

scholarly journals Space and time reconstructions in a posteriori analysis of evolution problems

ESAIM Proceedings â—˝  
10.1051/proc:072104 â—˝  
2007 â—˝  
Vol 21 â—˝  
pp. 31-44 â—˝  
Author(s):  
Charalambos Makridakis
Keyword(s):  
A Posteriori â—˝  
Evolution Problems â—˝  
Space And Time â—˝  
Posteriori Analysis â—˝  
A Posteriori Analysis

Exponential operators, generalized polynomials and evolution problems

2001 â—˝  
Vol 61 (2) â—˝  
pp. 99-108 â—˝  
Author(s):  
G Dattoli â—˝  
A.M Mancho â—˝  
M Quattromini â—˝  
A Torre
Keyword(s):  
Generalized Polynomials â—˝  
Evolution Problems

scholarly journals Justification of mean-field coupled modulation equations

1997 â—˝  
Vol 127 (3) â—˝  
pp. 639-650 â—˝  
Author(s):  
Guido Schneider
Keyword(s):  
Ground State â—˝  
Model Problem â—˝  
Mean Field â—˝  
Periodic Pattern â—˝  
Scaling Analysis â—˝  
Ginzburg Landau â—˝  
Modulation Equations â—˝  
Evolution Problems â—˝  
Ginzburg Landau Equations â—˝  
Infinite Line

We are interested in reflection symmetric (x↦–x) evolution problems on the infinite line. In the systems which we have in mind, a trivial ground state loses stability and bifurcates into a temporally oscillating, spatial periodic pattern. A famous example of such a system is the Taylor-Couette problem in the case of strongly counter-rotating cylinders. In this paper, we consider a system of coupled Kuramoto–Shivashinsky equations as a model problem for such a system. We are interested in solutions which are slow modulations in time and in space of the bifurcating pattern. Multiple scaling analysis is used in the existing literature to derive mean-field coupled Ginzburg–Landau equations as approximation equations for the problem. The aim of this paper is to give exact estimates between the solutions of the coupled Kuramoto–Shivashinsky equations and the associated approximations.

Sign in / Sign up

Export Citation Format

Share Document