TY  - GEN
N2  - This 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.
DO  - 10.1007/978-3-031-24583-1
DO  - doi
AB  - This 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.
T1  - Dual variational approach to nonlinear diffusion equations /
DA  - 2023.
CY  - Cham :
AU  - Marinoschi, Gabriela.
VL  - v.102
CN  - QA372
PB  - Birkhäuser,
PP  - Cham :
PY  - 2023.
ID  - 1461928
KW  - Differential equations, Nonlinear.
KW  - Burgers equation.
SN  - 9783031245831
SN  - 3031245830
TI  - Dual variational approach to nonlinear diffusion equations /
LK  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-24583-1
UR  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-24583-1
ER  -