Linear and nonlinear heat equations in $L^q_\delta$ spaces and universal bounds for global solutions

2001 ◽  
Vol 320 (1) ◽  
pp. 87-113 ◽  
Author(s):  
Marek Fila ◽  
Philippe Souplet ◽  
Fred B. Weissler
Keyword(s):  
Global Solutions ◽  
Heat Equations ◽  
Nonlinear Heat Equations ◽  
Linear And Nonlinear ◽  
Universal Bounds

scholarly journals Initial blow-up rates and universal bounds for nonlinear heat equations

2004 ◽  
Vol 196 (2) ◽  
pp. 316-339 ◽  
Author(s):  
Pavol Quittner ◽  
Philippe Souplet ◽  
Michael Winkler
Keyword(s):  
Blow Up ◽  
Heat Equations ◽  
Nonlinear Heat Equations ◽  
Universal Bounds

scholarly journals Blow-up of solutions of nonlinear heat equations

1988 ◽  
Vol 129 (2) ◽  
pp. 409-419 ◽  
Author(s):  
Luis A. Caffarrelli ◽  
Avner Friedman
Keyword(s):  
Blow Up ◽  
Heat Equations ◽  
Nonlinear Heat Equations

Sharp convolution and multiplication estimates in weighted spaces

2015 ◽  
Vol 13 (05) ◽  
pp. 457-480 ◽  
Author(s):  
Joachim Toft ◽  
Karoline Johansson ◽  
Stevan Pilipović ◽  
Nenad Teofanov
Keyword(s):  
Differential Equations ◽  
Stokes Equations ◽  
Weighted Spaces ◽  
Modulation Spaces ◽  
Local Analysis ◽  
Navier Stokes ◽  
Heat Equations ◽  
Navier Stokes Equations ◽  
Nonlinear Heat Equations ◽  
Hyperbolic Differential Equations

We establish sharp convolution and multiplication estimates in weighted Lebesgue, Fourier Lebesgue and modulation spaces. We cover, especially some results in [L. Hörmander, Lectures on Nonlinear Hyperbolic Differential Equations (Springer, Berlin, 1997); S. Pilipović, N. Teofanov and J. Toft, Micro-local analysis in Fourier Lebesgue and modulation spaces, II, J. Pseudo-Differ. Oper. Appl.1 (2010) 341–376]. The results are also related to some results by Iwabuchi in [T. Iwabuchi, Navier–Stokes equations and nonlinear heat equations in modulation spaces with negative derivative indices, J. Differential Equations248 (2010) 1972–2002].

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