Blow-up in reaction-diffusion equations with exponential and power-type nonlinearities

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Blow-up in reaction-diffusion equations with exponential and power-type nonlinearities. / Pulkkinen, Aappo.

Aalto University, 2011. 144 s.

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Pulkkinen A. Blow-up in reaction-diffusion equations with exponential and power-type nonlinearities. Aalto University, 2011. 144 s. (Aalto University publication series DOCTORAL DISSERTATIONS; 45).

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Pulkkinen, Aappo. / Blow-up in reaction-diffusion equations with exponential and power-type nonlinearities. Aalto University, 2011. 144 Sivumäärä

Bibtex - Lataa

@phdthesis{394ea2e5bbf04c559e2d62bcf90e0ecc,
title = "Blow-up in reaction-diffusion equations with exponential and power-type nonlinearities",
abstract = "In this dissertation we study blow-up phenomena in semilinear parabolic equations with both exponential and power-type nonlinearities. We study the behavior of the solutions as the blow-up moment in time and the blow-up point in space are approached. Our focus is on the supercritical case; however, we also give some results on the subcritical case. We prove results concerning the blow-up rate of solutions, and we obtain the blow-up profile for limit L1-solutions both with respect to the similarity variables and at the blow-up moment. We use techniques that are applicable both for the exponential and power nonlinearities. We also consider immediate regularization for minimal L1-solutions and improve on some earlier results. We are also interested in the behavior of selfsimilar solutions and we prove the existence of regular selfsimilar solutions that intersect the singular one arbitrary number of times.",
keywords = "semilinear parabolic equation, supercritical case, exponential nonlinearity, power-type nonlinearity, blow-up, selfsimilar solutions, blow-up rate, blow-up profile, regularity, semigroup estimates, semilinear parabolic equation, supercritical case, exponential nonlinearity, power-type nonlinearity, blow-up, selfsimilar solutions, blow-up rate, blow-up profile, regularity, semigroup estimates",
author = "Aappo Pulkkinen",
year = "2011",
language = "English",
isbn = "978-952-60-4138-4",
series = "Aalto University publication series DOCTORAL DISSERTATIONS",
publisher = "Aalto University",
number = "45",
school = "Aalto University",

}

RIS - Lataa

TY - THES

T1 - Blow-up in reaction-diffusion equations with exponential and power-type nonlinearities

AU - Pulkkinen, Aappo

PY - 2011

Y1 - 2011

N2 - In this dissertation we study blow-up phenomena in semilinear parabolic equations with both exponential and power-type nonlinearities. We study the behavior of the solutions as the blow-up moment in time and the blow-up point in space are approached. Our focus is on the supercritical case; however, we also give some results on the subcritical case. We prove results concerning the blow-up rate of solutions, and we obtain the blow-up profile for limit L1-solutions both with respect to the similarity variables and at the blow-up moment. We use techniques that are applicable both for the exponential and power nonlinearities. We also consider immediate regularization for minimal L1-solutions and improve on some earlier results. We are also interested in the behavior of selfsimilar solutions and we prove the existence of regular selfsimilar solutions that intersect the singular one arbitrary number of times.

AB - In this dissertation we study blow-up phenomena in semilinear parabolic equations with both exponential and power-type nonlinearities. We study the behavior of the solutions as the blow-up moment in time and the blow-up point in space are approached. Our focus is on the supercritical case; however, we also give some results on the subcritical case. We prove results concerning the blow-up rate of solutions, and we obtain the blow-up profile for limit L1-solutions both with respect to the similarity variables and at the blow-up moment. We use techniques that are applicable both for the exponential and power nonlinearities. We also consider immediate regularization for minimal L1-solutions and improve on some earlier results. We are also interested in the behavior of selfsimilar solutions and we prove the existence of regular selfsimilar solutions that intersect the singular one arbitrary number of times.

KW - semilinear parabolic equation

KW - supercritical case

KW - exponential nonlinearity

KW - power-type nonlinearity

KW - blow-up

KW - selfsimilar solutions

KW - blow-up rate

KW - blow-up profile

KW - regularity

KW - semigroup estimates

KW - semilinear parabolic equation

KW - supercritical case

KW - exponential nonlinearity

KW - power-type nonlinearity

KW - blow-up

KW - selfsimilar solutions

KW - blow-up rate

KW - blow-up profile

KW - regularity

KW - semigroup estimates

M3 - Doctoral Thesis

SN - 978-952-60-4138-4

T3 - Aalto University publication series DOCTORAL DISSERTATIONS

PB - Aalto University

ER -

ID: 21876289