• Previous Article
    Three dimensional system of globally modified Navier-Stokes equations with infinite delays
  • DCDS-B Home
  • This Issue
  • Next Article
    On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models
September  2010, 14(2): 629-654. doi: 10.3934/dcdsb.2010.14.629

Mutational inclusions: Differential inclusions in metric spaces

1. 

Institute of Mathematics, Johann Wolfgang Goethe University, 60054 Frankfurt (Main), Germany

Received  June 2009 Revised  September 2009 Published  June 2010

The focus of interest is how to extend ordinary differential inclusions beyond the traditional border of vector spaces. We aim at an existence theorem for solutions whose values are in a given metric space.
   In the nineties, Aubin suggested how to formulate ordinary differential equations and their main existence theorems in metric spaces: mutational equations (which are quite similar to the quasidifferential equations of Panasyuk). Now the well-known Antosiewicz-Cellina Theorem is extended to so-called mutational inclusions. It provides new results about nonlocal set evolutions in R N .
Citation: Thomas Lorenz. Mutational inclusions: Differential inclusions in metric spaces. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 629-654. doi: 10.3934/dcdsb.2010.14.629
[1]

Guy V. Norton, Robert D. Purrington. The Westervelt equation with a causal propagation operator coupled to the bioheat equation.. Evolution Equations & Control Theory, 2016, 5 (3) : 449-461. doi: 10.3934/eect.2016013

[2]

Thierry Horsin, Peter I. Kogut, Olivier Wilk. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions. Mathematical Control & Related Fields, 2016, 6 (4) : 595-628. doi: 10.3934/mcrf.2016017

[3]

Sebastián Ferrer, Martin Lara. Families of canonical transformations by Hamilton-Jacobi-Poincaré equation. Application to rotational and orbital motion. Journal of Geometric Mechanics, 2010, 2 (3) : 223-241. doi: 10.3934/jgm.2010.2.223

[4]

Manuel de León, Juan Carlos Marrero, David Martín de Diego. Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics. Journal of Geometric Mechanics, 2010, 2 (2) : 159-198. doi: 10.3934/jgm.2010.2.159

[5]

Thierry Horsin, Peter I. Kogut. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. I. Existence result. Mathematical Control & Related Fields, 2015, 5 (1) : 73-96. doi: 10.3934/mcrf.2015.5.73

[6]

Nguyen Huy Tuan, Mokhtar Kirane, Long Dinh Le, Van Thinh Nguyen. On an inverse problem for fractional evolution equation. Evolution Equations & Control Theory, 2017, 6 (1) : 111-134. doi: 10.3934/eect.2017007

[7]

Saulo R.M. Barros, Antônio L. Pereira, Cláudio Possani, Adilson Simonis. Spatially periodic equilibria for a non local evolution equation. Discrete & Continuous Dynamical Systems - A, 2003, 9 (4) : 937-948. doi: 10.3934/dcds.2003.9.937

[8]

Kerstin Does. An evolution equation involving the normalized $P$-Laplacian. Communications on Pure & Applied Analysis, 2011, 10 (1) : 361-396. doi: 10.3934/cpaa.2011.10.361

[9]

Viorel Barbu, Gabriela Marinoschi. An identification problem for a linear evolution equation in a banach space. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 1-12. doi: 10.3934/dcdss.2020081

[10]

Minkyu Kwak, Kyong Yu. The asymptotic behavior of solutions of a semilinear parabolic equation. Discrete & Continuous Dynamical Systems - A, 1996, 2 (4) : 483-496. doi: 10.3934/dcds.1996.2.483

[11]

Andrei Fursikov. The simplest semilinear parabolic equation of normal type. Mathematical Control & Related Fields, 2012, 2 (2) : 141-170. doi: 10.3934/mcrf.2012.2.141

[12]

Henri Berestycki, Juncheng Wei. On least energy solutions to a semilinear elliptic equation in a strip. Discrete & Continuous Dynamical Systems - A, 2010, 28 (3) : 1083-1099. doi: 10.3934/dcds.2010.28.1083

[13]

Stéphane Gerbi, Belkacem Said-Houari. Exponential decay for solutions to semilinear damped wave equation. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 559-566. doi: 10.3934/dcdss.2012.5.559

[14]

Shota Sato, Eiji Yanagida. Appearance of anomalous singularities in a semilinear parabolic equation. Communications on Pure & Applied Analysis, 2012, 11 (1) : 387-405. doi: 10.3934/cpaa.2012.11.387

[15]

Zhengce Zhang, Bei Hu. Gradient blowup rate for a semilinear parabolic equation. Discrete & Continuous Dynamical Systems - A, 2010, 26 (2) : 767-779. doi: 10.3934/dcds.2010.26.767

[16]

Maurizio Grasselli, Vittorino Pata. On the damped semilinear wave equation with critical exponent. Conference Publications, 2003, 2003 (Special) : 351-358. doi: 10.3934/proc.2003.2003.351

[17]

Martin Michálek, Dalibor Pražák, Jakub Slavík. Semilinear damped wave equation in locally uniform spaces. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1673-1695. doi: 10.3934/cpaa.2017080

[18]

Zhijian Yang, Zhiming Liu, Na Feng. Longtime behavior of the semilinear wave equation with gentle dissipation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (11) : 6557-6580. doi: 10.3934/dcds.2016084

[19]

Pavol Quittner. The decay of global solutions of a semilinear heat equation. Discrete & Continuous Dynamical Systems - A, 2008, 21 (1) : 307-318. doi: 10.3934/dcds.2008.21.307

[20]

Yang Cao, Jingxue Yin. Small perturbation of a semilinear pseudo-parabolic equation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 631-642. doi: 10.3934/dcds.2016.36.631

2018 Impact Factor: 1.008

Metrics

  • PDF downloads (8)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]