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Existence and nonexistence of solutions to nonlinear parabolic problems

Hisa Kotaro 東北大学

2020.03.25

概要

One of main subjects of research on partial differential equation is the well-posedness
of Cauchy problems, that is, existence of solutions, uniqueness of solutions and
dependence of initial data. In particular, it is significant to ask whether Cauchy
problems have solutions or not. Indeed, this question has attracted many interests
in the mathematical literature. The purpose of this thesis is to investigate the
threshold of the existence and the nonexistence of solutions to the Cauchy problems
for several nonlinear parabolic equations.
It is well-known that nonlinear parabolic problems often appear in the various
mathematical models such as heat transfer, chemical concentration, nonlinear radiation law and so on. The solvability of the nonlinear parabolic problems is taking
on complicated aspects; the solvability depends on a lot of factors such as diffusion effect, nonlinearity of equations, boundary conditions and the shape of initial
functions. This may be a reason why the issue has attracted much attention from
many mathematicians with development of the nonlinear analysis. ...

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