Critical dissipative estimate for a heat semigroup with a quadratic singular potential and critical exponent for nonlinear heat equations

DOI10.1016/j.jde.2018.08.030zbMath1422.35112OpenAlexW2886897604MaRDI QIDQ2423252

Norisuke Ioku, Takayoshi Ogawa

Publication date: 21 June 2019

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2018.08.030

zbMATH Keywords

nonlinear heat equationLorentz spacescritical estimatesinverse square potential

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (3)

Blow-up for Strauss type wave equation with damping and potential ⋮ The heat equation with strongly singular potentials ⋮ Probabilistic approach to the heat equation with a dynamic Hardy-type potential

Cites Work

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• Sharp decay estimates of \(L^q\)-norms for nonnegative Schrödinger heat semigroups
• Scale invariant elliptic operators with singular coefficients
• Existence and nonexistence of global solutions for \(u_ t = \Delta u + a(x)u^ p\) in \(\mathbb{R}^ d\)
• \(L^p\) norms of nonnegative Schrödinger heat semigroup and the large time behavior of hot spots
• Positive solutions and large time behaviors of Schrödinger semigroups, Simon's problem
• Non-uniqueness for second order elliptic operators
• Large time behaviors of hot spots for the heat equation with a potential
• The Fujita exponent for semilinear heat equations with quadratically decaying potential or in an exterior domain
• Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
• Large time asymptotics for fundamental solutions of diffusion equations
• Structure of positive solutions to \((-\Delta +V)u=0\) in \(R^ n\)
• Existence and non-existence of global solutions for a semilinear heat equation
• Comparison results for elliptic and parabolic equations via symmetrization: A new approach
• \(L^ p\) norms of non-critical Schrödinger semigroups
• On uniqueness and nonuniqueness of the positive Cauchy problem for parabolic equations with unbounded coefficients
• The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential
• Sharp decay estimates in Lorentz spaces for nonnegative Schrödinger heat semigroups
• Self-similar asymptotics of solutions to heat equation with inverse square potential
• Remarks on endpoint Strichartz estimates for Schrödinger equations with the critical inverse-square potential
• Sharp two-sided heat kernel estimates for critical Schrödinger operators on bounded domains
• On the Fujita exponent for a semilinear heat equation with a potential term
• Lp–Lq estimates for homogeneous operators
• Solvability of Nonlinear Schrödinger Equations with Some Critical Singular Potential via Generalized Hardy-Rellich Inequalities
• The Heat Equation with a Singular Potential
• Classical Fourier Analysis
• Weakly Differentiable Functions
• On the Cauchy Problem for Reaction-Diffusion Equations
• Strichartz estimates for the wave and Schroedinger equations with potentials of critical decay

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