Results of existence and uniqueness for the Cauchy problem of semilinear heat equations on stratified Lie groups

Initial value problems for second-order parabolic equations (35K15) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Semilinear parabolic equations (35K58)

Cites Work

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Quantization on nilpotent Lie groups
Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups
Solutions for semilinear parabolic equations in \(L^ p\) and regularity of weak solutions of the Navier-Stokes system
Besov spaces and Sobolev spaces on a nilpotent Lie group
Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation
Subelliptic estimates and function spaces on nilpotent Lie groups
Cauchy problem for semilinear parabolic equations with initial data in \(H_p^s(\mathbb{R}^n)\) spaces
Nonexistence results of solutions of semilinear differential inequalities on the Heisenberg group
Sobolev spaces on Lie groups: embedding theorems and algebra properties
An existence and uniqueness result for the Navier-Stokes type equations on the Heisenberg group
On nonlinear Schrödinger equations. II: \(H^ S\)-solutions and unconditional well-posedness
Local well-posedness for semilinear heat equations on H type groups
Existence and non-existence of global solutions for semilinear heat equations and inequalities on sub-Riemannian manifolds, and Fujita exponent on unimodular Lie groups
Sobolev algebras on Lie groups and Riemannian manifolds
Semi-Groups of Measures on Lie Groups
Stratified Lie Groups and Potential Theory for their Sub-Laplacians
A functional calculus for Rockland operators on nilpotent Lie groups
Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
Littlewood-Paley characterization of Hölder-Zygmund spaces on stratified Lie groups
Littlewood–Paley decompositions and Besov spaces on Lie groups of polynomial growth
Some Maximal Inequalities

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