Stability and correctness of abstract differential equations in Hilbert spaces
Jaroslav Barták (1978)
Czechoslovak Mathematical Journal
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Jaroslav Barták (1978)
Czechoslovak Mathematical Journal
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Marie-Françoise Bidaut-Véron, Quoc-Hung Nguyen (2015)
Journal of the European Mathematical Society
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El-Fiky, Ahmed (1998)
International Journal of Mathematics and Mathematical Sciences
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Piotr Biler (1995)
Studia Mathematica
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The existence of solutions to the Cauchy problem for a nonlinear parabolic equation describing the gravitational interaction of particles is studied under minimal regularity assumptions on the initial conditions. Self-similar solutions are constructed for some homogeneous initial data.
Kleber Carrapatoso (2014-2015)
Séminaire Laurent Schwartz — EDP et applications
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I present in this note recent results on the uniqueness and stability for the parabolic-parabolic Keller-Segel equation on the plane, obtained in collaboration with S. Mischler in [11].
Stefano Cardanobile, Delio Mugnolo (2008)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We apply functional analytical and variational methods in order to study well-posedness and qualitative properties of evolution equations on product Hilbert spaces. To this aim we introduce an algebraic formalism for matrices of sesquilinear mappings. We apply our results to parabolic problems of different nature: a coupled diffusive system arising in neurobiology, a strongly damped wave equation, and a heat equation with dynamic boundary conditions.
Eduard Rotenstein (2015)
Open Mathematics
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We study, in a Hilbert framework, some abstract parabolic variational inequalities, governed by reflecting subgradients with multiplicative perturbation, of the following type: y´(t)+ Ay(t)+0.t Θ(t,y(t)) ∂φ(y(t))∋f(t,y(t)),y(0) = y0,t ∈[0,T] where A is a linear self-adjoint operator, ∂φ is the subdifferential operator of a proper lower semicontinuous convex function φ defined on a suitable Hilbert space, and Θ is the perturbing term which acts on the set of reflecting directions, destroying...
Andrzej Raczyński (2004)
Banach Center Publications
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We study the existence of solutions to a nonlinear parabolic equation describing the temporal evolution of a cloud of self-gravitating particles with a given external potential. The initial data are in spaces of (generalized) pseudomeasures. We prove existence of local and global-in-time solutions, and also a kind of stability of global solutions.
Gekeler, Eckart (1979)
International Journal of Mathematics and Mathematical Sciences
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Henryk Leszczyński (1991)
Annales Polonici Mathematici
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Anna Pudełko (2005)
Annales Polonici Mathematici
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The Cauchy problem for an infinite system of parabolic type equations is studied. General operators of parabolic type of second order with variable coefficients are considered and the system is weakly coupled. We prove the existence and uniqueness of a bounded solution under Carathéodory type conditions and its differentiability, as well as the existence and uniqueness in the class of functions satisfying a natural growth condition. Both results are obtained by the fixed point method. ...
Piotr Biler (2006)
Banach Center Publications
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This note contains some remarks on the paper of Y. Naito concerning the parabolic system of chemotaxis and published in this volume.
R. Jeltsch (1979)
Numerische Mathematik
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