Del 102 - Progress in Nonlinear Differential Equations and Their Applications

Dual Variational Approach to Nonlinear Diffusion Equations

Inbunden, Engelska, 2023

AvGabriela Marinoschi

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This monograph explores a dual variational formulation of solutions to nonlinear diffusion equations with general nonlinearities as null minimizers of appropriate energy functionals. By reducing it to a minimization problem, the original problem is transformed into an optimal control problem with a linear state equation.

Produktinformation

Utgivningsdatum2023-03-29
Mått155 x 235 x 19 mm
Vikt518 g
FormatInbunden
SpråkEngelska
SerieDel 102 i Progress in Nonlinear Differential Equations and Their Applications
Antal sidor212
FörlagBirkhauser Verlag AG
ISBN9783031245824

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Gabriela Marinoschi is a senior scientific researcher with Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy and full member of the Romanian Academy. Her research interests focus on the analysis and control of evolution equations in infinite dimensional spaces and include the application of variational and semigroup methods as well as the control techniques to mathematical models based on partial differential equations, especially for those describing physical and biological processes.

Introduction.- Nonlinear Diffusion Equations with Slow and Fast Diffusion.- Weakly Coercive Nonlinear Diffusion Equations.- Nonlinear Diffusion Equations with a Noncoercive Potential.- Nonlinear Parabolic Equations in Divergence Form with Wentzell Boundary Conditions.- A Nonlinear Control Problem in Image Denoising.- An Optimal Control Problem for a Phase Transition Model.- Appendix.- Bibliography.- Index.