The first 50 years for applicable analysis

In 1972, I came upon the idea to begin a journal on Applied Analysis. It was not to be another engineering mathematics journal, nor we want it to be just another analysis journal. The stress was to be on analysis which could have a direct application to the equations of mathematical physics. What came to mind at that time were nonlinear and linear integral equations partial differential equations of mixed type, shock waves, solitons, generalized functions, Sobolev spaces, quantum field theory, function analytic methods for partial differential equations, and some theoretical methods for numerical analysis.

Applicable Analysis has brought out Special Issues of the journal from time-to-time. These have been either to honor distinguished mathematicians upon achieving an advanced birthday or to have a collection of papers on a particular mathematical topic we are interested in promoting. In both cases, this brought in some very interesting papers. For these special Issues, we had Guest Editors I now list several special issues and the Guest Editors by name.

• In Memory of Carlo Pucci, Guest Editors, Volume 85 Issue 1–3: (2006).

• Analysis and Applications of Partial Differential Equations in Biomathematics, Guest Editors Jumping Shi and Xingfu Zou, Volume 89 Issue 7: (2010).

• Regularization Theory and Applications, Guest Editors Bernd Hofmann and Masahiro Yamamoto, Volume 89, Issue 11, (2010).

• On a Class of Generalized Functions Arising in Elasticity, Guest Editor Yu. V. Egorov, Volume, 90 Issue 11 (2011).

• Mathematical and Numerical Analysis of Flow and Transport in Porous Media, Guest Editor Brahim Amaziane and Mladen Jurak, Volume 95 Issue 10, (2016).

• Variational Analysis, Optimization and Optimal Control, Guest Editors Jen-Chih Yao, Der-Chen Chang, Robert P. Gilbert and Yongzhi Steve Xu, Volume 94, Issue 1, (2015).

• Inverse Problems and Regularization Theory, Guest Editor Jin Cheng and Masahiro Yamamoto, Shuai Lu, Jens Flemming and Steven W. Anzengruber, Volume 94, Issue 3, (2015).

• Upscaling in Engineering and Biology, Guest Editor Grigory Panasenko, Volume 95, Issue 7, (2016).

• Multiscale Inverse Problems, Guest Editor Adrian Muntean, Volume 97 Issue 1, (2018).

• Mathematical Contact Mechanics, Guest Editors Laetitia Paoli and Meir Shillor, Volume 97, Issue 8, (2018)

• In Memory of Vassily Vassilievich Zhikov. Guest Editors Grigori Panasenko, Robert P. Gilbert and Alexander Pankov, Volume 98 , Issue 1–2, (2019).

Applicable Analysis has been a success in that way too many papers are submitted. Associate Editors (AE) now frequently have to turn papers away since the Associate Editors feel that these papers do not meet the high standards of our journal. I have to admit that added to this is that cottage industries have sprouted up that turn out many papers which are written just because they can be written. I believe that most journals also are plagued with this problem. However, there are many very innovative papers out there with new uses of analysis and these we would be anxious to have submitted. Tastes have changed and many topics that were only in nascent development fifty years ago are now in full bloom. Some of these areas are homogenization, inverse problems, moving boundary problems. Some areas we should like to attract are peri-dynamic methods, dynamic rather than kinetic bio-mathematics papers, stochastic optimal control, optimal control, interacting particle systems, numerical functional analysis, contact problems, ill-posed problems, optimal control of electrodynamic phenomena, differential-geometric methods in cosmology.

Here is to the 100-year Jubilee of Applicable Analysis.

Disclosure statement

No potential conflict of interest was reported by the author.