Book Review: Solution of continuous nonlinear PDEs through order completion
نویسندگان
چکیده
منابع مشابه
Arbitrary Continuous Nonlinear PDEs through the Order Completion Method
In 1994 we showed that very large classes of systems of nonlinear PDEs have solutions which can be assimilated with usual measurable functions on the Euclidean domains of definition of the respective equations. Recently, the regularity of such solutions has significantly been improved by showing that they can in fact be assimilated with Hausdorff continuous functions. The method of solution of ...
متن کاملHausdorff Continuous Solutions of Nonlinear PDEs through the Order Completion Method
It was shown in [13] that very large classes of nonlinear PDEs have solutions which can be assimilated with usual measurable functions on the Euclidean domains of definition of the respective equations. In this paper the regularity of these solutions has significantly been improved by showing that they can in fact be assimilated with Hausdorff continuous functions. The method of solution of PDE...
متن کاملThe Order Completion Method for Systems of Nonlinear PDEs Revisited
In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion as presented in (Oberguggenberger and Rosinger, 1994). In particular, spaces of generalized functions are constructed that contain generalized solutions to a large class of systems of continuous, nonlinear PDEs. In terms of the existence and uniqueness results previously obtained for ...
متن کاملexistence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types
بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی بیان شده اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...
15 صفحه اولThe Order Completion Method for Systems of Nonlinear PDEs: Solutions of Initial Value Problems
and Applied Analysis 3 With respect to the pointwise order u ≤ v ⇐⇒ ( ∀x ∈ Ω : u (x) ≤ v (x) ) (11) the setNL(Ω) is a Dedekind complete lattice. In particular, the supremum and infimum of a setA ⊂ NL(Ω) is given by inf A = (I ∘ S) (φ) , (12) supA = (I ∘ S) (ψ) , (13) respectively, where φ : Ω ∋ x → inf{u(x) : u ∈ A} and ψ : Ω ∋ x → sup{u(x) : u ∈ A}. Furthermore, the lattice NL(Ω) is fully di...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1996
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-96-00620-9