Existence of weak solutions for abstract hyperbolic‐parabolic equations
Marcondes Rodrigues Clark
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Published: Apr 19, 1993
DOI: 10.1155/s0161171294001067
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In this paper we study the Existence and Uniqueness of solutions for the following Cauchy problem: urn:x-wiley:01611712:media:ijmm283109:ijmm283109-math-0001 urn:x-wiley:01611712:media:ijmm283109:ijmm283109-math-0002 where A 1 and A 2 are bounded linear operators in a Hilbert space H , { A ( t )} 0≤ t ≤ T is a family of self‐adjoint operators, M is a non‐linear map on H and f is a function from (0, T ) with values in H . As an application of problem (1) we consider the following Cauchy problem: urn:x-wiley:01611712:media:ijmm283109:ijmm283109-math-0003 urn:x-wiley:01611712:media:ijmm283109:ijmm283109-math-0004 where Q is a cylindrical domain in ℝ 4 ; k 1 and k 2 are bounded functions defined in an open bounded set Ω ⊂ ℝ 3 , urn:x-wiley:01611712:media:ijmm283109:ijmm283109-math-0005 where a i j and are bounded functions on Ω and f is a function from (0, T ) with values in L 2 ( Ω ).
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