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Partial Differential Equations in Applied Mathematics provides a platform for the rapid circulation of original researches in applied mathematics and applied sciences by utilizing partial differential equations and related techniques.

Differential equations, Partial --- Differential equations, Partial. --- Partial differential equations --- differential equations --- boundary problems --- non-linear analysis --- applied mathematics

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Boundary value problems. --- Differential equations, Elliptic. --- Singularities (Mathematics). --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Singularities (Mathematics) --- Boundary conditions (Differential equations) --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Geometry, Algebraic --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Differential equations, Linear --- Differential equations, Partial

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This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.

Topological Groups. --- Potential theory (Mathematics). --- Differential equations, partial. --- Harmonic analysis. --- Functional analysis. --- Global differential geometry. --- Topological Groups, Lie Groups. --- Potential Theory. --- Partial Differential Equations. --- Abstract Harmonic Analysis. --- Functional Analysis. --- Differential Geometry. --- Geometry, Differential --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Groups, Topological --- Continuous groups --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Partial differential equations --- Topological groups. --- Lie groups. --- Partial differential equations. --- Differential geometry. --- Differential geometry --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Lie groups --- Potential theory (Mathematics) --- Harmonic analysis --- Functional analysis

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This open access book deals with a rich variety of taxis-type cross-diffusive equations. Particularly, it intends to show the key role played by quasi-energy inequality in the derivation of some necessary a priori estimates. This book addresses applied mathematics and all researchers interested in mathematical development of reaction-diffusion theory and its application and can be a basis for a graduate course in applied mathematics.

Boundary value problems. --- Chemotaxis --- Navier-Stokes equations. --- Mathematical models. --- Equations, Navier-Stokes --- Differential equations, Partial --- Fluid dynamics --- Viscous flow --- Chemiotaxis --- Chemotropism --- Biochemistry --- Growth --- Taxes (Biology) --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Problemes de contorn --- Quimiotaxi --- Models matemàtics --- Equacions de Navier-Stokes --- Navier-Stokes (Equacions) --- Dinàmica de fluids --- Equacions en derivades parcials --- Models (Matemàtica) --- Models experimentals --- Models teòrics --- Mètodes de simulació --- Anàlisi de sistemes --- Mètode de Montecarlo --- Modelització multiescala --- Models economètrics --- Models lineals (Estadística) --- Models multinivell (Estadística) --- Models no lineals (Estadística) --- Programació (Ordinadors) --- Simulació per ordinador --- Teoria de màquines --- Models biològics --- Bioquímica --- Creixement --- Problemes de valor límit --- Equacions diferencials --- Física matemàtica --- Funcions de variables complexes --- Dispersió (Matemàtica) --- Equacions de Von Kármán --- Problema de Dirichlet --- Problema de Neumann --- Problemes de Riemann-Hilbert --- Problemes de valor inicial --- Reaction-Diffusion --- Haptotaxis --- Navier-Stokes --- Cancer invasion --- Coral fertilization --- Sensity-suppressed motility --- Oncolytic virotherapy --- Foraging scrounging interplay