Reduction operators of linear second-order parabolic equations
نویسندگان
چکیده
منابع مشابه
Reduction Operators of Linear Second-Order Parabolic Equations
The reduction operators, i.e., the operators of nonclassical (conditional) symmetry, of (1 + 1)dimensional second order linear parabolic partial differential equations and all the possible reductions of these equations to ordinary differential ones are exhaustively described. This problem proves to be equivalent, in some sense, to solving the initial equations. The “no-go” result is extended to...
متن کاملOn the stability of linear differential equations of second order
The aim of this paper is to investigate the Hyers-Ulam stability of the linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$ $fin C[a,b]$ and $-infty
متن کاملDoubling properties for second order parabolic equations
We prove the doubling property of L-caloric measure corresponding to the second order parabolic equation in the whole space and in Lipschitz domains. For parabolic equations in the divergence form, a weaker form of the doubling property follows easily from a recent result, the backward Harnack inequality, and known estimates of Green’s function. Our method works for both the divergence and nond...
متن کاملDifferential Transformations of Parabolic Second-Order Operators in the Plane
The theory of transformations for hyperbolic second-order equations in the plane, developed by Darboux, Laplace and Moutard, has many applications in classical differential geometry [12, 13], and beyond it in the theory of integrable systems [14, 19]. These results, which were obtained for the linear case, can be applied to nonlinear Darboux-integrable equations [2, 7, 15, 16]. In the last deca...
متن کاملLinear Elliptic Equations of Second Order
The classical Schauder type results on C-regularity of solutions are exposed for linear second order elliptic equations with Hölder coefficients. Our approach is based on equivalent seminorms in Hölder spaces C, which are similar to seminorms introduced by S. Campanato [1]. Under this approach, the C-estimates for solutions are derived from the maximum principle and the interior smoothness of h...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2008
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/41/18/185202