Partial Differential Equations and Applications

Dear Colleagues,

This Special Issue of Mathematics entitled “Partial Differential Equations and Applications” will be a collection of approximately half expository and half unpublished research papers. The goal is to provide both students and practitioners, or scholars working in different areas, with knowledge of the problems, tools, and most recent developments in Partial Differential Equations (PDEs) and Applications.

All aspects of Partial Differential Equations, both linear and non-linear, will be covered, as well as Partial Differential Operators (PDOs), with emphasis on the dynamics adopted by these solutions. In addition, articles concerning the applications of PDEs to mathematical, physical, social, and computational sciences will be presented.

The following is a list of topics that will be covered: well-posedness; existence/uniqueness; qualitative properties of the solutions; boundary-value problems; bifurcation and chaotic behavior; special solutions (e.g., orthogonal polynomials); integrability; PDEs on manifolds; heat flow; spectral properties of PDOs; kernels; representation of solutions on a particular basis; inverse problems; differential algebra (algebras of PDOs, commutativity, algebraic varieties corresponding to ideals, and differential Galois theory); stochastic PDEs; differential-difference equations; real/complex numbers domain.

We aim to collect expository papers that review essential definitions and techniques, explain the history of the area if appropriate, and review contemporary developments, covering the above-mentioned topics divided into the following areas: solutions; integrability; dynamics; spectral properties; algebraic aspects; complex domain; stochastic PDEs; differential-difference PDEs; applications to a vast array of sciences.

MSC 2010: 35-XX, 58Bxx, 58Jxx, 60H15

Prof. Dr. Emma Previato
Guest Editor

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