Phase space analysis of semilinear parabolic equations

DOI10.1016/j.jfa.2014.05.007zbMath1296.35225arXiv1308.1909OpenAlexW2962849491MaRDI QIDQ2253209

Fabio Nicola

Publication date: 25 July 2014

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.1909

zbMATH Keywords

Cauchy problempseudodifferential operatorsmodulation spaceslocal well-posednesssemilinear parabolic equations

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Degenerate parabolic equations (35K65) Hilbert spaces of continuous, differentiable or analytic functions (46E20) Semilinear parabolic equations (35K58)

Related Items

Propagation of exponential phase space singularities for Schrödinger equations with quadratic Hamiltonians ⋮ Gabor frames of Gaussian beams for the Schrödinger equation ⋮ Modulation spaces and non-linear Hartree type equations ⋮ An introduction to the Gabor wave front set ⋮ Propagation of Gabor singularities for semilinear Schrödinger equations ⋮ Well‐posedness of generalized KdV and one‐dimensional fourth‐order derivative nonlinear Schrödinger equations for data with an infinite L² norm ⋮ The Cauchy problem for the Hartree type equation in modulation spaces ⋮ Estimates on modulation spaces for Schrödinger operators with time-dependent sub-linear vector potentials ⋮ Phase space analysis of the Hermite semigroup and applications to nonlinear global well-posedness ⋮ On the well-posedness for a class of pseudo-differential parabolic equations ⋮ The Cauchy problem for non-linear higher order Hartree type equation in modulation spaces ⋮ On dissipative nonlinear evolutional pseudo-differential equations ⋮ On the local well-posedness of the nonlinear heat equation associated to the fractional Hermite operator in modulation spaces ⋮ Propagation of the Gabor wave front set for Schrödinger equations with non-smooth potentials ⋮ Schrödinger equations with rough Hamiltonians

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