Partial Differential EquationsCambridge University Press, 21 mei 1987 - 518 pagina's This book is a rigorous introduction to the abstract theory of partial differential equations. The main prerequisite is familiarity with basic functional analysis: more advanced topics such as Fredholm operators, the Schauder fixed point theorem and Bochner integrals are introduced when needed, and the book begins by introducing the necessary material from the theory of distributions and Sobolev spaces. Using such techniques, the author presents different methods available for solving elliptic, parabolic and hyperbolic equations. He also considers the difference process for the practical solution of a partial differential equation, emphasising that it is possible to solve them numerically by simple methods. Many examples and exercises are provided throughout, and care is taken to explain difficult points. Advanced undergraduates and graduate students will appreciate this self-contained and practical introduction. |
Inhoudsopgave
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adjoint apply Theorem assumptions b₁ B₂ Banach spaces belongs boundary conditions boundary value operators boundary value problem bounded c₁ c₂ coefficients compact Condition 11.1 cone cone condition consider continuous convergence coordinates Corollary define Definition dense derivatives differential equations Dirichlet problem Dirichlet system distribution dm(s eigenvalues elliptic differential operator embedding equivalent estimate Example exists finite Fourier transformation Fredholm operator functions g₁ Gelfand triple gives Green's formula hence Hilbert space implies inequality integral L₂ L₂(N Lemma linear Neumann problem norm normal obtain partition of unity prove regulariser regularity theorems satisfied self-adjoint sequence sesquilinear form Sobolev spaces solvable spectral theorem strongly elliptic subset subspace supp Suppose T₁ Theorem 4.1 trace operator U₁ W½(N weak equation Y₁ ym(t yo(x zero ди ду дф