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pro vyhledávání: '"Laister, Robert"'
We consider the Cauchy problem for fractional semilinear heat equations with supercritical nonlinearities and establish both necessary conditions and sufficient conditions for local-in-time solvability. We introduce the notion of a dilation-critical
Externí odkaz:
http://arxiv.org/abs/2308.05240
We study necessary conditions and sufficient conditions for the existence of local-in-time solutions of the Cauchy problem for superlinear fractional parabolic equations. Our conditions are sharp and clarify the relationship between the solvability o
Externí odkaz:
http://arxiv.org/abs/2204.08243
Publikováno v:
In Journal de mathématiques pures et appliquées June 2024 186:150-175
Autor:
Laister, Robert, Sierzega, Mikolaj
Publikováno v:
Mathematische Annalen 381 (2021) pp. 75-90
We derive a blow-up dichotomy for positive solutions of fractional semilinear heat equations on the whole space. That is, within a certain class of convex source terms, we establish a necessary and sufficient condition on the source for all positive
Externí odkaz:
http://arxiv.org/abs/1912.01537
Autor:
Laister, Robert, Sierzega, Mikolaj
Publikováno v:
Annales de l'Institut Henri Poincar\'e C, Analyse non lin\'eaire 37 (3), 2020, 709-725
The problem of obtaining necessary and sufficient conditions for local existence of non-negative solutions in Lebesgue spaces for semilinear heat equations having monotonically increasing source term $f$ has only recently been resolved (Laister et al
Externí odkaz:
http://arxiv.org/abs/1911.10530
Publikováno v:
Annales de l'Institut Henri Poincar\'e - Analyse Non-Lin\'eaire, 33 (6). pp. 1519-1538 (2016)
We consider the scalar semilinear heat equation $u_t-\Delta u=f(u)$, where $f\colon[0,\infty)\to[0,\infty)$ is continuous and non-decreasing but need not be convex. We completely characterise those functions $f$ for which the equation has a local sol
Externí odkaz:
http://arxiv.org/abs/1407.2444
Akademický článek
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We give a simple proof of a lower bound for the Dirichlet heat kernel in terms of the Gaussian heat kernel. Using this we establish a non-existence result for semilinear heat equations with zero Dirichlet boundary conditions and initial data in $L^q(
Externí odkaz:
http://arxiv.org/abs/1307.6688
Publikováno v:
Journal of Differential Equations, 255 (10) 2013, pp. 3020-3028. ISSN 0022-0396
We establish non-existence results for the Cauchy problem of some semilinear heat equations with non-negative initial data and locally Lipschitz, nonnegative source term $f$. Global (in time) solutions of the scalar ODE $\dot v=f(v)$ exist for $v(0)>
Externí odkaz:
http://arxiv.org/abs/1303.7183
Publikováno v:
In Comptes rendus - Mathématique July-August 2014 352(7-8):621-626