TAILIEUCHUNG - Periodic solutions for evolution equations

This article is organized as follows. First we analyze the one dimensional case. Necessary and su cient conditions for the existence and uniqueness of periodic solutions are shown. Results for sub(super)-periodic solutions are proved as well in this case. In the next section we show that the same existence result holds for linear symmetric maximal monotone operators on Hilbert spaces. In the last section the case of non-linear sub-di erential operators is considered. | Electronic Journal of Differential Equations Monogrpah 03 2002. ISSN 1072-6691. URL http or http ftp login ftp Periodic solutions for evolution equations Mihai Bostan Abstract We study the existence and uniqueness of periodic solutions for evolution equations. First we analyze the one-dimensional case. Then for arbitrary dimensions finite or not we consider linear symmetric operators. We also prove the same results for non-linear sub-differential operators A dip where is convex. Contents 1 Introduction 1 2 Periodic solutions for one dimensional evolution equations 2 Uniqueness . 2 Existence. 5 Sub super -periodic solutions. 10 3 Periodic solutions for evolution equations on Hilbert spaces 16 Uniqueness . 17 Existence. 17 Periodic solutions for the heat equation . 31 Non-linear case. 34 1 Introduction Many theoretical and numerical studies in applied mathematics focus on permanent regimes for ordinary or partial differential equations. The main purpose of this paper is to establish existence and uniqueness results for periodic solutions in the general framework of evolution equations x0 t Ax t f t t 2 R 1 Mathematics Subject Classifications 34B05 34G10 34G20. Key words maximal monotone operators evolution equations Hille-Yosida s theory. 2002 Southwest Texas State University. Submitted May 14 2002. Published August 23 2002. 1 2 Periodic solutions for evolution equations by using the penalization method. Note that in the linear case a necessary condition for the existence is hf i T f t dt 2 Range A . 2 Unfortunately this condition is not always sufficient for existence see the example of the orthogonal rotation of R2. Nevertheless the condition 2 is sufficient in the symmetric case. The key point consists of considering first the perturbed equation t x a t Axa t f t t 2 R where a 0. By using the Banach s fixed point theorem we deduce the existence and uniqueness of the periodic .

• Sinh học
• dimensional evolution
• Periodic solutions
• evolution equations
• Hilbert spaces
• Periodic solutions
• heat equation
• Cohesive zone model
• Stress gradient
• Crack evolution
• Two dimensional elastic structures
• Non uniform stress
• Báo cáo khoa học
• báo cáo y học
• công trình nghiên cứu về y học
• tài liệu về y học
• cách trình bày báo cáo
• Regularization of a Cauchy problem for the heat equation
• Cauchy problem for the heat equation
• A priori conditions
• Different a priori conditions
• Quasi reversibility method
• Weak solution
• Exponential nonlinearity
• Semilinear heat equation
• Galerkin approximation
• question of heat transfer
• heat transfer techniques
• methods of heat transfer
• heat transfer equation
• heating metal
• welding technology
• non linear
• Anisotropic hyperbolic heat equation
• Sobolev spaces
• Integral transforms
• Vector valued distributions
• Irregular distributions
• Stability estimate
• Regularization method
• Inverse source problem
• Unknown source term
• Heat equation in the Banach space L1(Rn)
• Interpolation spaces
• General solution
• Interpolation method
• Initial value boundary
• Smooth boundary first
• Heat Transfer Modes
• Conduction Equation
• Extended Surfaces
• Flow equations
• boundary layer
• Heat Exchangers
• Chemistry
• Mechanical engineering systems
• Heat energy
• Heat energy supplied
• Internal combustion engines
• The steady flow energy equation
• Units used in this book
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• Backward heat problem
• Modified quasi Boundary value method
• Polar coordinates
• Ill posed problem
• Non Fourier Conduction
• Harmonic Boundary Conditions
• Hyperbolic asymmetric heat
• Thermal displacement equation
• Long hollow cylinder
• Mathematical modeling of temperature
• Analytical and numerical solution
• Transient heat conduction equation
• Bimodal shaped laser beam
• Finite element modeling
• Power law type long memory behaviours
• Fractional models
• Cauer networks
• Foster networks
• Zeros geometric distributions
• Functional analysis
• Partial differential equations
• Boundary value problems
• Miscellaneous complements
• he heat equation
• Breast tumour
• Neural network
• Thermal pattern
• Finite element model
• Pennes bio heat equation