Partial Differential Inequalities with Nonlinear Convolution Terms

Free Download Marius Ghergu, "Partial Differential Inequalities with Nonlinear Convolution Terms "
English | ISBN: 3031218558 | 2022 | 144 pages | PDF | 2 MB
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.
Read more