LEADER 03417nam 2200541 450 001 9910686790303321 005 20240115155521.0 010 $a9783031245831$b(electronic bk.) 010 $z9783031245824 024 7 $a10.1007/978-3-031-24583-1 035 $a(MiAaPQ)EBC7221154 035 $a(Au-PeEL)EBL7221154 035 $a(OCoLC)1374426207 035 $a(DE-He213)978-3-031-24583-1 035 $a(PPN)269093052 035 $a(EXLCZ)9926347443300041 100 $a20230730d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDual variational approach to nonlinear diffusion equations /$fGabriela Marinoschi 205 $a1st ed. 2023. 210 1$aCham, Switzerland :$cSpringer,$d[2023] 210 4$d©2023 215 $a1 online resource (223 pages) 225 1 $aPNLDE Subseries in Control,$x2731-7374 ;$v102 311 08$aPrint version: Marinoschi, Gabriela Dual Variational Approach to Nonlinear Diffusion Equations Cham : Springer Basel AG,c2023 9783031245824 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- 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. 330 $aThis monograph explores a dual variational formulation of solutions to nonlinear diffusion equations with general nonlinearities as null minimizers of appropriate energy functionals. The author demonstrates how this method can be utilized as a convenient tool for proving the existence of these solutions when others may fail, such as in cases of evolution equations with nonautonomous operators, with low regular data, or with singular diffusion coefficients. By reducing it to a minimization problem, the original problem is transformed into an optimal control problem with a linear state equation. This procedure simplifies the proof of the existence of minimizers and, in particular, the determination of the first-order conditions of optimality. The dual variational formulation is illustrated in the text with specific diffusion equations that have general nonlinearities provided by potentials having various stronger or weaker properties. These equations can represent mathematical models to various real-world physical processes. Inverse problems and optimal control problems are also considered, as this technique is useful in their treatment as well. 410 0$aPNLDE Subseries in Control,$x2731-7374 ;$v102 606 $aBurgers equation 606 $aDifferential equations, Nonlinear 606 $aEquacions diferencials no lineals$2thub 608 $aLlibres electrònics$2thub 615 0$aBurgers equation. 615 0$aDifferential equations, Nonlinear. 615 7$aEquacions diferencials no lineals 676 $a260 700 $aMarinoschi$b Gabriela$0517203 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910686790303321 996 $aDual Variational Approach to Nonlinear Diffusion Equations$93087616 997 $aUNINA