A comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups
TLDR
In this paper, a comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups is presented, and blow-up type results and global in t -boundedness of solutions of nonlinear equations for the heat p -sub-Laplacian on stratified Lie groups are obtained.Abstract:
In this paper we present a comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups. Moreover, using the comparison principle we obtain blow-up type results and global in t -boundedness of solutions of nonlinear equations for the heat p -sub-Laplacian on stratified Lie groups.read more
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Existence and non-existence of global solutions for semilinear heat equations and inequalities on sub-Riemannian manifolds, and Fujita exponent on unimodular Lie groups
TL;DR: In this paper , the authors studied the global well-posedness of the following Cauchy problem on a sub-Riemannian manifold, where LM is a sub Laplacian of the manifold.
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Existence and non-existence of global solutions for semilinear heat equations and inequalities on sub-Riemannian manifolds, and Fujita exponent on unimodular Lie groups
TL;DR: In this paper, the authors studied the global well-posedness of the Cauchy problem on a sub-Riemannian manifold M and obtained a critical Fujita exponent for 1 p ∞ and some positive u 0 ∈ L q (G ) with 1 ≤ q ∞.
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Compact embeddings, eigenvalue problems, and subelliptic Brezis–Nirenberg equations involving singularity on stratified Lie groups
TL;DR: In this paper , the authors studied the eigenvalue problem for the fractional p -sub-Laplacian over the fractionally Folland-Stein-Sobolev spaces on stratified Lie groups and proved the existence of at least two weak solutions via the Nehari manifold technique.
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Dynamical analysis of rational and semi‐rational solution for a new extended (3 + 1)‐dimensional Kadomtsev‐Petviashvili equation
TL;DR: In this article , a new extended (3 + 1)dimensional Kadomtsev-Petviashvili equation is proposed that portrays a unique dispersion effect about x,z,x,z $$ , and its integrability is confirmed via the WTC-Kruskal algorithm in Painlevé sense.
References
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Book
Stratified Lie groups and potential theory for their sub-Laplacians
TL;DR: In this paper, the fundamental solution for a sub-Laplacian and applications of potential theory for sub-laplacians are discussed. But the analysis of the potential theory is not discussed.
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Caracterisation des operateurs hypoelliptiques homogenes
Bernard Helffer,J. Nourrigat +1 more
TL;DR: In this article, Caracterisation des operateurs hypoelliptiques homogenes is described for partial differential equation (PDE) based homogenization of homogenizations.
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On horizontal Hardy, Rellich, Caffarelli–Kohn–Nirenberg and p-sub-Laplacian inequalities on stratified groups
TL;DR: In this paper, a version of horizontal weighted Hardy-Rellich type and Caffarelli-Kohn-Nirenberg type inequalities on stratified groups and their consequences are studied.
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