A Liouville theorem for vector-valued nonlinear heat equations and applications

2000 ◽  
Vol 316 (1) ◽  
pp. 103-137 ◽  
Author(s):  
Frank Merle ◽  
Hatem Zaag
Keyword(s):  
Liouville Theorem ◽  
Heat Equations ◽  
Nonlinear Heat Equations ◽  
Vector Valued

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

scholarly journals A Liouville Theorem for Superlinear Heat Equations on Riemannian Manifolds

2019 ◽  
Vol 87 (2) ◽  
pp. 303-313 ◽  
Author(s):  
Daniele Castorina ◽  
Carlo Mantegazza ◽  
Berardino Sciunzi
Keyword(s):  
Riemannian Manifolds ◽  
Liouville Theorem ◽  
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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