Degenerate parabolic equations appearing in atmospheric dispersion of pollutants
Electronic Journal of Qualitative Theory of Differential Equations, 2016 Linear and nonlinear degenerate abstract parabolic equations with variable coefficients are studied. Here the equation and boundary conditions are degenerated on all boundary and contain some parameters.
Veli Shakhmurov, Aida Sahmurova
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Asynchronous exponential growth of semigroups of nonlinear operators
Journal of Mathematical Analysis and Applications, 1992 The authors analyze the property of asynchronous exponential growth for the abstract nonlinear differential equation \(z'(t)= Az(t)+ F(z(t))\), \(t\geq 0\), \(z(0)= x\in X\), where \(A\) is the infinitesimal generator of a semigroup of linear operators in the Banach space \(X\) and \(F\) is a nonlinear operator in \(X\). Asynchronous exponential growth
Gyllenberg, M, Webb, G.F
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A Spectral Mapping Theorem and Invariant Manifolds for Nonlinear Schr\"odinger Equations [PDF]
, 1999 A spectral mapping theorem is proved that resolves a key problem in applying invariant manifold theorems to nonlinear Schr\" odinger type equations. The theorem is applied to the operator that arises as the linearization of the equation around a standing
Gesztesy, F. +3 more
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Physiologically structured populations with diffusion and dynamic boundary conditions [PDF]
, 2011 We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. The model is equipped with generalized Wentzell-Robin (or dynamic) boundary conditions.
Farkas, J. Z., Hinow, P.
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Single-Mode and Dual-Mode Nongomogeneous Dissipative Structures in the Nonlocal Model of Erosion
Моделирование и анализ информационных систем, 2015 We consider a periodic boundary-value problem for a nonlinear equation with the deviating spatial argument in the case when the deviation is small. This equation is called a spatially nonlocal erosion equation.
A. M. Kovaleva, D. A. Kulikov
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Myopic Models of Population Dynamics on Infinite Networks [PDF]
, 2013 Reaction-diffusion equations are treated on infinite networks using semigroup methods. To blend high fidelity local analysis with coarse remote modeling, initial data and solutions come from a uniformly closed algebra generated by functions which are ...
Carlson, Robert
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On continuity of solutions for parabolic control systems and input-to-state stability [PDF]
, 2018 We study minimal conditions under which mild solutions of linear evolutionary control systems are continuous for arbitrary bounded input functions.
Jacob, Birgit +2 more
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Existence of Pseudo Almost Periodic Solutions to Some Classes of Partial Hyperbolic Evolution Equations [PDF]
, 2006 The paper examines the existence of pseudo almost periodic solutions to some classes of partial hyperbolic evolution equations. Namely, sufficient conditions for the existence and uniqueness of pseudo almost periodic solutions to those classes of ...
Diagana, Toka
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Parabolic theory of the discrete p-Laplace operator [PDF]
, 2013 We study the discrete version of the $p$-Laplacian. Based on its variational properties we discuss some features of the associated parabolic problem.
Mugnolo, Delio
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Convergence and approximation of semigroups of nonlinear operators in Banach spaces
Journal of Functional Analysis, 1972 AbstractA general convergence theorem for semigroups of nonlinear operators in a general Banach space is proved. It is then applied to obtain an approximation theorem for such semigroups. These results extend the previously known results for semigroups of linear operators in Banach space.
Brezis, H, Pazy, A
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