Geometric theory of semilinear parabolic equations. (English) Zbl 0456.35001

Henry, Dan

Lecture Notes in Mathematics. 840. Berlin-Heidelberg-New York: Springer-Verlag. IV, 348 p. (1981).

MSC:

35-02	Research exposition (monographs, survey articles) pertaining to partial differential equations
35B10	Periodic solutions to PDEs
35B35	Stability in context of PDEs
35K55	Nonlinear parabolic equations
35B30	Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35K60	Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35B40	Asymptotic behavior of solutions to PDEs
35B15	Almost and pseudo-almost periodic solutions to PDEs
35B50	Maximum principles in context of PDEs
34G20	Nonlinear differential equations in abstract spaces
45D05	Volterra integral equations
47E05	General theory of ordinary differential operators
47F05	General theory of partial differential operators
80A25	Combustion
92D25	Population dynamics (general)

Keywords:

geometric theory; semilinear parabolic equations; equilibrium points; periodic solutions; almost periodic solutions; invariant manifolds; asymptotical behavior; ordinary differential equation; Volterra integral equations; unbounded operators; linearization of equations; decomposition; Lyapunov functions; maximum principle arguments; contraction maps; analytic semigroup theory; theory of boundary problems; sectorial operators; existence and uniqueness theorems; abstract differential equations in a Banach space; gradient flow problems; bifurcations; transfer of stability; Gronwall’s lemma; linear evolution families; Poincare map; population genetics; combustion