naa a22 4500 510760937 CHVBK 20180411083139.0 cr unu---uuuuu 180411e20130701xx s 000 0 eng 10.1007/s13163-012-0108-9 doi (NATIONALLICENCE)springer-10.1007/s13163-012-0108-9 Supersolutions for a class of semilinear heat equations [Elektronische Daten] [James Robinson, Mikołaj Sierżęga] A semilinear heat equation $$u_{t}=\Delta u+f(u)$$ with nonnegative measurable initial data is considered under the assumption that $$f$$ is nonnegative and nondecreasing and $$\Omega \subseteq \mathbb R ^{n}$$ . A simple technique for proving existence and regularity based on the existence of supersolutions is presented, then a method of construction of local and global supersolutions is proposed. This approach is then applied to the model case $$f(s)=s^{p}$$ with initial data in $$L^{q}(\Omega )$$ , for which an extension of the monotonicity-based existence argument is offered for the critical case ( $$n(p-1)/2=q>1$$ ) in all dimensions. New sufficient conditions for the existence of local and global classical solutions are derived in the critical and subcritical ( $$n(p-1)/2 q>1$$ ) range of parameters. Some possible generalisations of the method to a broader class of equations are discussed. Universidad Complutense de Madrid, 2012 Nonlinear heat equation nationallicence Reaction-diffusion equation nationallicence Singular data nationallicence Supersolutions nationallicence Regularity nationallicence Existence nationallicence Global solutions nationallicence Robinson James Mathematics Institute, University of Warwick, Zeeman Building, CV4 7AL, Coventry, UK aut Sierżęga Mikołaj Mathematics Institute, University of Warwick, Zeeman Building, CV4 7AL, Coventry, UK aut Revista Matemática Complutense Springer Milan 26/2(2013-07-01), 341-360 1139-1138 26:2<341 2013 26 13163 https://doi.org/10.1007/s13163-012-0108-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13163-012-0108-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Robinson James Mathematics Institute, University of Warwick, Zeeman Building, CV4 7AL, Coventry, UK aut NATIONALLICENCE 700 1- Sierżęga Mikołaj Mathematics Institute, University of Warwick, Zeeman Building, CV4 7AL, Coventry, UK aut NATIONALLICENCE 773 0- Revista Matemática Complutense Springer Milan 26/2(2013-07-01), 341-360 1139-1138 26:2<341 2013 26 13163 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer