Research On Semigroups Of Operators And Applications To The Model Of Temperature Field Of Artillery Barrel Wall

This thesis is devoted to investigating mainly semigroups of operators andsome applications to neutral partial functional di?erential equations and evo-lution equations. Also, combining with theory of semigroups of operators andpartial di?erential equations, the model of temperature field in artillery barrelwall is studied. This thesis consists of ten chapters.The first chapter introduces the research background, methods, contents andresults of this thesis.Chapter 2 is preliminaries, mainly including some definitions and basic prop-erties on strongly continuous semigroups, integrated semigroups and pseudo al-most automorphic functions.Chapter 3 introduces the concept and characterizes the properties of n-timesintegrated Laplace transforms of O(ω(t)) vector-valued functions. Based on theseproperties, chapter 3 establishes Hille-Yosida type theorems for O(ω(t)) n-timesintegrated semigroups.With the help of integrated semigroups, chapter 4 investigates the regularityof solutions for the following partial neutral functional di?erential equations withfinite delay ?and obtains the su?cient and necessary conditions for its integral solution tobecome strict solution, where A : D(A)→X is a nondensely defined Hille-Yosida operator, L is a bounded linear operator from CX = C([?r,0],X) to Xsuch that R(L) ? D(A) , F is a nonlinear continuous operator from CX to X.For t≥0, xt : [?r,0]→X is defined as Using integrated semigroups, in chapter 5 we investigate the regularity andstability of solutions for the following partial neutral functional di?erential equa-tions with infinite delayand obtain the su?cient and necessary conditions for its integral solution tobecome strict solution, and the necessary conditions for its solution semigroupto be stable, where A is a nondensely defined Hille-Yosida operator on a Banachspace X endowed with the norm·, B is a seminormed linear space of functionsmapping (?∞,0] to X and satisfies some fundamental axioms, F and G arenonlinear continuous operators from B to X. For every t≥0, xt is a functionmapping (?∞,0] into X which is defined byBy means of strongly continuous semigroups, chapter 6 establishes su?cientconditions for the existence and uniqueness of pseudo almost automorphic mildsolutions to evolution equationwhere A is the infinitesimal generator of exponentially stable strongly continuoussemigroups T(t)t≥0 on a Banach space X, B,C are bounded linear operators onX, f : R×X→X, g : R×X→X are pseudo almost automorphic.Chapter 7 obtains su?cient conditions for the existence and uniqueness ofpseudo almost automorphic mild solutions to evolution equationwhere A is a sectorial linear operator on a Banach space X andσ(A)∩iR = ?,B,C are bounded linear operators on Xα, f : R×X→Xβ, g : R×X→X arepseudo almost automorphic. Chapter 8 aims to establish the existence and uniqueness theorems of pseudoalmost automorphic mild solutions to the following nonautonomous evolutionequations with Stepanov-like pseudo almost automorphic termswhere A(t) satisfy"Acquistapace?Terreni"conditions, evolution family (U(t,s))t≥sgenerated by A(t) has exponential dichotomy, Green's functionΓ(t,s) is bi-almostautomorphic, B,C(t,s)t≥s are bounded linear operators, h, f, F are Stepanov-like pseudo almost automorphic for p > 1 and continuous.Combining with theory of semigroups of operators and di?erential equations,chapter 9 is on the model of temperature field of artillery barrel wall, obtainingthe analytic solutions to the heat-controlled di?erential equations of compositematerial barrel wall.Chapter 10 is devoted to summing up the whole thesis.