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Partial Differential Inequalities with Nonlinear Convolution Terms (Paperback, 1st ed. 2022)
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Partial Differential Inequalities with Nonlinear Convolution Terms (Paperback, 1st ed. 2022)
Series: SpringerBriefs in Mathematics
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This brief research monograph uses modern mathematical methods to
investigate partial differential equations with nonlinear
convolution terms, enabling readers to understand the concept of a
solution and its asymptotic behavior. In their full generality,
these inequalities display a non-local structure. Classical
methods, such as maximum principle or sub- and super-solution
methods, do not apply to this context. This work discusses partial
differential inequalities (instead of differential equations) for
which there is no variational setting. This current work brings
forward other methods that prove to be useful in understanding the
concept of a solution and its asymptotic behavior related to
partial differential inequalities with nonlinear convolution terms.
It promotes and illustrates the use of a priori estimates, Harnack
inequalities, and integral representation of solutions. One of the
first monographs on this rapidly expanding field, the present work
appeals to graduate and postgraduate students as well as to
researchers in the field of partial differential equations and
nonlinear analysis.
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