نتایج جستجو برای: stochasic evolution equations
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where the constant a is non-zero. However, (1.1) can be reduced to the standard evolution equation (3.4) in an appropriate space because the operator I − a∂2 x which acts on ∂tu(x, t) can be inverted. Thus, (1.1) is an example of a regular equation; we study such problems in Section 2. Section 3 is concerned with those regular equations of a special form suggested by (1.1). Another example whic...
In the spirit of the recent work of Ibragimov [1] who adopted the infinitesimal method for calculating invariants of families of differential equations using the equivalence groups, we apply the method to evolution type equations of the form ut = f(x, u)uxx + g(x, u, ux). We show that the equivalence Lie algebra admitted by this equation has two functionally independent differential invariants ...
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