Abstract quasilinear parabolic equations
Copyright policy )Abstract quasilinear parabolic equations
The author deals with an abstract quasilinear parabolic problem \(u'(t)=A(t,u(t))u(t)+f(t,u(t)), t>0\), \(u(0)=u_ 0\) in a Banach space X. His theorems on existence and uniqueness are such that a concrete quasilinear parabolic problem can be attacked without imposing growth conditions on the coefficients. Regularity results are obtained by means of interpolation spaces based on infinitesimal generators of bounded semi-groups. The characterization of those spaces in classical analytical terms are given.
- DigiZeitschriften Germany
- Scuola Normale Superiore Italy
- University of Parma Italy
interpolation spaces, bounded semi- groups, Smoothness and regularity of solutions to PDEs, existence, Initial value problems for linear higher-order PDEs, uniqueness, Nonlinear differential equations in abstract spaces, Semigroups of nonlinear operators, abstract quasilinear parabolic problem, Article, Higher-order parabolic equations, Regularity, 510.mathematics, General existence and uniqueness theorems (PDE), infinitesimal generators
interpolation spaces, bounded semi- groups, Smoothness and regularity of solutions to PDEs, existence, Initial value problems for linear higher-order PDEs, uniqueness, Nonlinear differential equations in abstract spaces, Semigroups of nonlinear operators, abstract quasilinear parabolic problem, Article, Higher-order parabolic equations, Regularity, 510.mathematics, General existence and uniqueness theorems (PDE), infinitesimal generators
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