Results 21 to 30 of about 6,505 (230)
Study of the Existence of Supersolutions for Nonlocal Equations with Gradient Terms [PDF]
Milan Journal of Mathematics, 2020 23 pages, 6 ...
Begoña Barrios, Leandro M. Del Pezzo
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The method of supersolutions for semilinear heat equations with unbounded initial data [PDF]
Revista Matemática Complutense, 2011 A semilinear heat equation $u_{t}=Δu+f(u)$ with nonnegative initial data in a subset of $L^{1}(Ω)$ is considered under the assumption that $f$ is nonnegative and nondecreasing and $Ω\subseteq \R^{n}$. A simple technique for proving existence and regularity based on the existence of supersolutions is presented, then a method of construction of local and
James C. Robinson, Mikołaj Sierżęga
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A supersolutions perspective on hypercontractivity [PDF]
Annali di Matematica Pura ed Applicata (1923 -), 2020 The purpose of this article is to expose an algebraic closure property of supersolutions to certain diffusion equations. This closure property quickly gives rise to a monotone quantity which generates a hypercontractivity inequality. Our abstract argument applies to a general Markov semigroup whose generator is a diffusion and satisfies a curvature ...
Aoki, Yosuke +5 more
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Optimal Sub- or Supersolutions in Reaction-Diffusion Problems
Journal of Differential Equations, 2002 The author considers the semilinear parabolic problem \[ \begin{aligned} & {{\partial u}\over{\partial t}} = \Delta u + f(u) \quad\text{in}\quad \Omega\times(0,T), \\& {{\partial u}\over{\partial n}} + g(u) = 0 \quad\text{on}\quad \partial\Omega\times(0,T), \\ & u(x,0) = u_0(x),\end{aligned}\tag \(*\) \] where \(\Omega\) is a sufficiently smooth ...
R. Sperb
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Supersolutions for a class of nonlinear parabolic systems [PDF]
Journal of Differential Equations, 2015 In this paper, by using scalar nonlinear parabolic equations, we construct supersolutions for a class of nonlinear parabolic systems including $$ \left\{\begin{array}{ll} \partial_t u=Δu+v^p,\qquad & x\inΩ,\,\,\,t>0,\\ \partial_t v=Δv+u^q, & x\inΩ,\,\,\,t>0,\\ u=v=0, & x\in\partialΩ,\,\,\,t>0,\\ (u(x,0), v(x,0))=(u_0(x),v_0(x ...
Kazuhiro Ishige +2 more
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Plurisubharmonic envelopes and supersolutions [PDF]
Journal of Differential Geometry, 2019 We make a systematic study of (quasi-)plurisubharmonic envelopes on compact Kähler manifolds, as well as on domains of $\mathbb{C}^n$, by using and extending an approximation process due to Berman [Ber13]. We show that the quasi-psh envelope of a viscosity super-solution is a pluripotential super-solution of a given complex Monge-Ampère equation.
Vincent Guedj +2 more
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Supersolutions to degenerated logistic equation type [PDF]
, 2014 In this work we provide a method for building up a strictly positive supersolution for the steady state of a degenerated logistic equation type, i.e., when the weight function vanishes on the boundary of the domain. This degenerated system is related in obtaining the so-called large solutions.
Marcos Marvá
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Minimal supersolutions of BSDEs with lower semicontinuous generators [PDF]
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2014 We study the existence and uniqueness of minimal supersolutions of backward stochastic differential equations with generators that are jointly lower semicontinuous, bounded below by an affine function of the control variable and satisfy a specific normalization property.
Heyne, Gregor +2 more
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Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in the annulus [PDF]
Opuscula Mathematica, 2015 In this paper, we establish existence and asymptotic behavior of a positive classical solution to the following semilinear boundary value problem: \[-\Delta u=q(x)u^{\sigma }\;\text{in}\;\Omega,\quad u_{|\partial\Omega}=0.\] Here \(\Omega\) is an annulus
Safa Dridi, Bilel Khamessi
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Electronic Journal of Qualitative Theory of Differential Equations, 2021 In this paper we show existence and multiplicity of positive solutions using the sub-supersolution method and Mountain Pass Theorem in a general singular system which the operator is not homogeneous neither linear.
Suellen Arruda, Rubia Nascimento
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