Second order Cauchy problem with a damping operator.
On the book ``Branded lectures in mathematics'' by Marek Zakrzewski
The content of the book thus covers the basic issues of a fairly broadly defined field of mathematical analysis and in the author's opinion, ,,... can serve as a basic textbook for students of technical universities, as well as a supplemental textbook for students of mathematics, especially future teachers of this subject matter''.
Evolution equations with parameter in the hyperbolic case
The purpose of this paper is to give theorems on continuity and differentiability with respect to (h,t) of the solution of the initial value problem du/dt = A(h,t)u + f(h,t), u(0) = u₀(h) with parameter in the “hyperbolic” case.
Second order evolution equations with parameter
We give some theorems on continuity and differentiability with respect to (h,t) of the solution of a second order evolution problem with parameter . Our main tool is the theory of strongly continuous cosine families of linear operators in Banach spaces.
Regularity of domains of parameterized families of closed linear operators
The purpose of this paper is to provide a method of reduction of some problems concerning families of linear operators with domains to a problem in which all the operators have the same domain . To do it we propose to construct a family of automorphisms of a given Banach space X having two properties: (i) the mapping is sufficiently regular and (ii) for t ∈ . Three effective constructions are presented: for elliptic operators of second order with the Robin boundary condition with a parameter;...
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