A Liouville theorem for ancient solutions to a semilinear heat equation and its elliptic counterpart
, 2020 We establish the nonexistence of nontrivial ancient solutions to the nonlinear heat equation $u_t=\Delta u+|u|^{p-1}u$ which are smaller in absolute value than the self-similar radial singular steady state, provided that the exponent $p$ is strictly ...
Sourdis, Christos
core
Maximum principles for a class of nonlinear second order elliptic differential equations [PDF]
Applicable Analysis, (62) (1996), 1998 In this paper we investigate maximum principles for functionals defined on solutions to special partial differential equations of elliptic type, extending results by Payne and Philippin. We apply such maximum principles to investigate one overdetermined problem.
arxiv
Pinching estimates and motion of hypersurfaces by curvature functions [PDF]
arXiv, 2004 Second derivative pinching estimates are proved for a class of elliptic and parabolic equations, including motion of hypersurfaces by curvature functions such as quotients of elementary symmetric functions of curvature. The estimates imply convergence of convex hypersurfaces to spheres under these flows, improving earlier results of B.
arxiv
On Absolutely Minimizing Lipschitz Extensions and PDE $Δ_infty = 0$ [PDF]
arXiv, 2004 We prove the existence of Absolutely Minimizing Lipschitz Extensions by a method which differs from those used by G. Aronsson in general metrically convex compact metric spaces and R. Jensen in Euclidean spaces. Assuming Jensen's hypotheses, our method yields numerical schemes for computing, in euclidean $\mathbb R$, the solution of viscosity of ...
arxiv
A compactness result for a Gelfand-Liouville system with Lipschitz condition
, 2015 We give a quantization analysis to an elliptic system (Gelfand-Liouville type system) with Dirichlet condition.
Bahoura, Samy Skander
core
On generalized Sobolev algebras and their applications [PDF]
arXiv, 2005 In the last two decades, many algebras of generalized functions have been constructed, particularly the so-called generalized Sobolev algebras. Our goal is to study the latter and some of their main properties. In this framework, we pose and solve a nonlinear degenerated Dirichlet problem with irregular data such as Dirac generalized functions.
arxiv
Dynamical properties of single species stage structured model with Michaelis-Menten type harvesting on adult population and linear harvesting on juvenile population. [PDF]
Heliyon, 2023 Akter S, Islam MS, Hossain T.
europepmc +1 more source
Harnack type inequality on Riemannian manifolds of dimension 5
, 2013 We give some estimates of type sup * inf on Riemannian manifold of dimension 5.Comment: 12 pages.
Bahoura, Samy Skander +1 more
core +1 more source
A boundary point lemma for Black-Scholes type operators [PDF]
Comm. Pure Appl. Anal. 5 (2006), 505-514, 2005 We prove a sharp version of the Hopf boundary point lemma for Black-Scholes type equations. We also investigate the existence and the regularity of the spatial derivative of the solutions at the spatial boundary.
arxiv
Pointwise monotonicity of heat kernels. [PDF]
Rev Mat Complut, 2023 Alonso-Orán D +3 more
europepmc +1 more source